The response of equity prices to monetary policy announcements: Decomposing the announcement day return into cash-flow news, interest rate news, and risk premium news

Journal Pre-proofs The response of equity prices to monetary policy announcements: Decomposing the announcement day return into cash-flow news, interest rate news, and risk premium news Olaf Stotz PII: DOI: Reference:

S0261-5606(18)30682-X https://doi.org/10.1016/j.jimonfin.2019.102069 JIMF 102069

To appear in:

Journal of International Money and Finance

Please cite this article as: O. Stotz, The response of equity prices to monetary policy announcements: Decomposing the announcement day return into cash-flow news, interest rate news, and risk premium news, Journal of International Money and Finance (2019), doi: https://doi.org/10.1016/j.jimonfin.2019.102069

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier Ltd.

The response of equity prices to monetary policy announcements: Decomposing the announcement day return into cash-flow news, interest rate news, and risk premium news. Olaf Stotz Abstract This paper analyzes how US stock prices respond to monetary policy decisions. On days of FOMC meetings, we decomposed the daily stock market return into cash-flow news, interest rate news, and risk premium news by applying a novel approach which uses information from option prices. The empirical results suggest that the relation between monetary policy surprises and stock returns is state dependent: In expansions (recessions), the cash-flow channel (risk premium channel) explains most of the announcement day returns. However, during time periods with unconventional monetary policy instruments, the risk premium channel has become more important, even in expansions. Key words: Monetary policy news, stock returns, return decomposition, announcement days JEL classification: E5, G12

Corresponding Author: Olaf Stotz, Professor of Finance (Asset Management), Frankfurt School of Finance & Management, Adickesallee 32-34, D-60322 Frankfurt, phone: ++49 69 154008769, email: [email protected]

1

The response of equity prices to monetary policy announcements: Decomposing the announcement day return into cash-flow news, interest rate news, and risk premium news. Abstract This paper analyzes how US stock prices respond to monetary policy decisions. On days of FOMC meetings, we decomposed the daily stock market return into cash-flow news, interest rate news, and risk premium news by applying a novel approach which uses information from option prices. The empirical results suggest that the relation between monetary policy surprises and stock returns is state dependent: In expansions (recessions), the cash-flow channel (risk premium channel) explains most of the announcement day returns. However, during time periods with unconventional monetary policy instruments, the risk premium channel has become more important, even in expansions.

Key words: Monetary policy news, stock returns, return decomposition, announcement days JEL classification: E5, G12

1. Introduction The question of how monetary policy (MP) affects stock prices has been extensively analyzed. The main conclusion is that an unexpected fall in interest rates is followed by a rise in stock prices. For example, in the US, Bernanke and Kuttner (2005) showed that for days when the Federal Open Market Committee (FOMC) meets and gives a statement on the current MP, an unexpected fall in short-term interest rates of 25 basis points is followed by a stock market increase of roughly 100 basis points. Stock prices can change because cash-flow expectations are revised and/or different discount rates (the riskfree rate plus the risk premium) are applied to those expectations. The question of which of the three components explains the stock market’s return on FOMC announcement days has been investigated less thoroughly. Without knowing how MP announcements are related to the three components of a stock return, the various channels through which MP influences capital markets and, finally, the real economy cannot

2

be fully understood. Consider, for example, the wealth effect of MP. According to this effect, higher stock prices lead to a rise in consumption and increasing economic activity (see Ando and Modigilani, 1963). If this increase is driven by discount rate news, higher stock prices today are accompanied by lower expected returns in the future. Such a wealth effect on consumption may be temporary as lower future returns imply lower future consumption growth. That is, the increase in wealth (consumption) today “borrows” returns (consumption) from the future. In contrast, if the rise in stock prices is driven by cash-flow news, the increase in consumption may be permanent as future returns are unaffected. Accordingly, the wealth effect implies a higher rate of future consumption growth if stock prices are driven by cash-flow news than if they are driven by discount-rate news.1 In this paper, we decompose the announcement day (a-day) return of the stock market into its three components (Campbell, 1991): Cash-flow news, news about the term structures of interest rates (derived from US Treasury bond yields), and risk premium news. The identification of the three components of daily stock returns is not feasible with common methods, like the predictive regression approach (e.g., the vector autoregressive approach of Campbell and Ammer, 1993), as daily stock returns are almost unforecastable. Therefore, we propose a new method to decompose daily stock returns by using information from option markets. Option prices reflect opinions and information from market participants and fully absorb current expectations about the distribution of future stock returns at different points in time. In particular, the approach consists of two steps. First, using option-pricing theory, a risk-neutral probability density function (PDF) for future stock prices is obtained from option prices. In the second step, the risk-neutral PDF needs to be transformed into a real (i.e., risk-adjusted) PDF to calculate the expected return. This transformation, however, requires the specification of investor preferences (e.g., Ait-Sahalia, 2000; Ross, 2015). We assume an investor with power utility and follow Kang and Kim (2006) in our empirical implementation. We call this estimate of the expected stock return the “option-implied return” (OIR). In our sensitivity section, we also evaluate alternative

Other transmission effects of MP, such as Tobin’s q (Tobin, 1969), the risk-taking effect of Borio and Zhu (2012), and the balance-sheet effect of Bernanke and Gertler (1989), might also be differentially affected by permanent cash-flow news and temporary discount rate news. In particular, the risk-taking effect seems to be important as certain unconventional instruments of US monetary policy attempt to change the risk premium and, therefore, the risk-taking behavior of market participants. We analyze the impact of unconventional monetary policy instruments in Section 4.2. 1

3

preference functions and show that the OIR approach delivers rather robust conclusions about the monetary-policy-stock-return-relation (hereafter MP-SR). The OIR can be calculated for different return horizons as options with different maturities reflect opinions about the PDF of a stock price at different points in time. Accordingly, the OIR approach produces a term structure of expected stock returns, which is required by the decomposition approach of Campbell (1991). Given the OIR term structure, cash-flow expectations can then be backed up within the decomposition framework quite easily. We apply the OIR approach for the US stock market for daily returns over a 21-year period (from 1997 to 2017) and obtain the following results. First, we find that – on average – lower-than-expected interest rates are related to an increase in stock prices. This largely confirms the results of previous literature. Second, looking at the three components of stock returns, this relation is mainly driven by cash-flow news. Third, the MP-SR is driven by the three news components differently in expansion and recession periods. During expansion periods, if interest rates are lowered unexpectedly by 25 basis points, stock prices tend to rise by 225 bps, of which 268 bps can be attributed to higher cash-flow expectations. During recessions, in contrast, an unexpected fall in interest rates of 25 bps is accompanied by a decrease in stock prices of almost 42 bps. Of this decrease, only 7 bps can be explained by higher cash-flow expectations and more than 86 bps can be attributed to a higher risk premium.2 The remaining part is based on falling interest rates. Thus, the MP-SR differs substantially in sign and composition. How can this reversal in the relation between unexpected stock returns and unexpected MP decisions be explained? During expansion periods, unexpectedly lower (higher) interest rates may boost (weaken) the economy, leading to higher (lower) cash-flow expectations. Thus, MP decisions may control the growth rate of the economy by setting short-term interest rates (i.e., a controlling effect). During recession periods, however, lower interest rates set by the Federal Reserve (FED) may signal an economic condition worse than expected and, accordingly, investors require higher risk premiums following an unexpected interest rate cut (i.e., a signaling effect). The increasing role of such a risk premium explanation in the MP-SR has also been observed in the years after the start of the financial crisis in 2008. During this time period, MP implemented unconventional instruments, such as buying

2

As the US economy is usually in a non-recession period, the unconditional slope estimate is smaller than zero as documented previously (e.g., Bernanke and Kuttner, 2005).

4

long-term bonds or extending the length of a zero-interest rate environment. The empirical results imply that during this time period, the MP-SR is predominantly understood by the risk premium channel, even in expansion periods. These results are compatible with the risk-taking effect of Borio and Zhu (2012), especially in the post-2008 period when the FED introduced unconventional monetary policy instruments. In sum, our paper adds two main contributions to the MP-SR literature. The first is methodological: We use option prices to identify cash-flow news, interest rate news and risk premium news in daily stock returns and relate them to MP news on a-days. The second is empirical: We demonstrate that the decomposition of the MP-SR can be characterized by a controlling effect in expansions and a signaling effect in recessions. Also, in the years after the financial crisis in 2008, the risk-taking effect has become more important. Overall, decomposing the stock market’s price reaction on a-days delivers a more detailed description of the MP-SR and a better understanding how MP announcements are perceived by the stock market. The rest of the paper is organized as follows: Section 2 describes the methodology and introduces the OIR approach. Empirical results are presented in Section 3. Robustness checks are undertaken in Section 4. Section 5 concludes our article.

2. Methodology In the first part of this section, we begin with a short description of how the MP-SR is usually analyzed (regression of stock returns on MP surprises). Thereby, we show how the decomposed stock returns are considered and present an extended regression approach. The second part then describes how the three components of unexpected stock returns (cash-flow news, interest rate news and risk premium news) are derived from option prices.

2.1 Regression analysis The relation between MP-SR is primarily evaluated by estimating the following regression (see, for example, Bernanke and Kuttner, 2005):

5

Rt 1  a  b  NMPt 1   t 1 ,

(1)





where Rt 1  100  ln  St 1  Dt 1   ln  St  is the stock market return from t to t+1 in bps and NMPt 1 is the unexpected news component of the monetary policy during the same period. We follow Kuttner (2001) and measure unexpected monetary policy news by using changes in the federal funds futures,





NMPt  D ( D  d )  f m ,t  f m ,t 1 , where f m ,t is the federal funds future price in t expiring in month m, D is the number of days in this month and d is the a-day in this month. A negative sign for NMP indicates an expansionary monetary policy (i.e., falling interest rates) and vice versa.3 Typically, an expansionary monetary policy is associated with rising stock prices, which results in negative estimates of the slope parameter, b, but this slope can vary considerably depending on the time period analyzed (e.g., Chulia et al., 2010; Kontonikas et al., 2013). If the expected stock market return, denoted by Et  Rt 1  , varies over time, equation (1) needs to be modified:

URt 1  Rt 1  Et  Rt 1 

(2)

 aUR  bUR  NMPt 1   t 1 ,

where URt 1 is the unexpected return. A stock price can change unexpectedly because cash-flow expectations are revised and/or investors apply different discount rates to those cash-flow expectations. Campbell and Shiller (1988) derive a loglinear version of the dividend discount model that allows for the decomposition of the unexpected stock return into a cash-flow news component and discount-rate news. The discount-rate news can be further split into a news component, reflecting unexpected changes in interest rates, and risk premiums (see Campbell, 1991). Then, the unexpected return is equivalent to: 





i 0

i 0

i 0

URt 1   Et 1  Et    i cft 1 i   Et 1  Et    i rft 1 i   Et 1  Et    i rpt 1 i

(3)

 NCFt 1  NRFt 1  NRPt 1 ,

In Section 3.4 we also consider non-conventional MP instruments. Following Hanson and Stein (2015), we use the two-year US government bond yield to capture the changes in expectations regarding the path of the federal funds rate over several quarters. 3

6

where NCFt 1 reflects unexpected news about future cash-flows (i.e., dividends) between t and t+1,

NRFt 1 reflects unexpected news surrounding the term structure of interest rates (i.e., yields of US Treasury bonds), and NRPt 1 reflects unexpected news with respect to the term structure of the equity risk premium.  is a parameter obtained from the linearization of the dividend discount model (see Campbell and Shiller, 1988).4 The left-hand side of equation (2) can be replaced by using the decomposition in equation (3):

NCFt  NRFt  NRPt  aUR  bUR  NMPt   t .

(4)

Equation (4) states that unexpected monetary policy can be associated with the unexpected stock return through three channels: Cash-flow news, interest rate news, and risk premium news. In order to gain a better understanding of the importance of those channels, we assess the following system of equations:

N t  A  B  NMPt  Εt ,

(5)

where N t   NCFt ,  NRFt ,  NRPt  and NMPt   NMPt , NMPt , NMPt  . A, B, and Ε are the '

'

corresponding vectors of regression parameters. We estimate the system of equations in (5) employing the seemingly unrelated regressions (SUR) approach of Zellner (1962). In a SUR system, the sum of the '

 NRF NCF , b  NRP  is equivalent to the parameter, bUR , in (2), that is elements in vector B  b , b

b NCF  b  NRF  b  NRP  bUR . This approach therefore decomposes the commonly estimated slope parameter and permits a more detailed interpretation of how MP affects stock prices. The results from estimates of equations (5) will provide a framework for describing the MP-SR. We call this approach the decomposition of the MP-SR.

4

In the empirical analysis, expectations are formed for different points in future time (i = 1, 3, 6, 9, 12, 18, 24 months). Therefore, the parameter, , is set to 0.997 for changes in monthly expected returns following previous studies (e.g., Campbell, 1991). However, these expectations are revised on a daily basis; thus, E t 1  E t  reflects daily changes in expectations (see also Appendix A for more details).

7

2.2 The term structure of expected stock returns derived from option prices A main empirical challenge in estimating equation (5) is to find an appropriate proxy for the term structure of expected stock market returns in order to derive unexpected changes in it. This section describes the OIR approach, which employs option prices to acquire those expectations. The estimation of OIR is realized in two steps. During the first step, a risk-neutral probability density function (PDF) is calculated. We estimate the risk-neutral PDF with the option price model of Black and Scholes. Using this model is necessary as option prices from major databases are using Black/Scholes implied volatilities. This step has been applied since the 1970s (e.g., Cox and Ross, 1976a,b). Second, the risk-neutral PDF has to be risk-adjusted in order to obtain “real” or “risk-adjusted” probabilities. Obtaining a real PDF requires an assumption on investor preferences (e.g., Ross, 2015). * Let f t ( ST ) be the real PDF of a stock price in T with information at t. f t ( ST ) is the corresponding risk-

neutral PDF. U t (Ct ) denotes the preferences over consumption. Ait-Sahalia and Lo (2000) have shown that in equilibrium, the two PDFs are related to each other as follows:

ft ( ST )  ft * ( ST )  exp  (T  t ) 

U 't (CT ) . U 'T (CT )

(6)

In the case of power utility preferences, i.e.,

C1 U (C )  , 1 

(7)

where  is the coefficient of risk aversion, Kang and Kim (2006) show that risk-neutral PDF can be transformed into a real PDF as follows:

ft ( ST ) 

ST  ft * ( ST )

x



 ft * ( x)dx

.

(8)

From Equation (8), the expected stock price at different points in time can be easily obtained. To compute the expected return, expected dividends between t and t+T have to be considered. Let





PVt Dt ,T represent the present value at time, t, of expected dividends between t and T. According to the

put/call

parity

of

European

stock

options

(Stoll,

1969),

this

term

is

8





PVt Dt ,T  Putt  Callt  St  PV  X T  . Thereby, PVt  X T  is the present value at time, t, of





exercise price, X, of an option with maturity, T. Defining Qt ,T  1  PVt Dt ,T / Pt , a number smaller but close to one, we can make use of Equation (8) and the present value of dividends to calculate the option-implied return (OIR) – a measure for the expected rate of return – as: 

 

Et  rT   OIRt ,T    ft  ST   ln  ST  dST   ln  St   ln Qt ,T .

(9)

0

Equation (9) provides the framework to derive the term structure of expected stock returns from option prices. Subtracting the risk-free interest rate from the expected return yields the risk premium,

Et  rT   rft ,T  Et  rpT  . Knowing the term structures of the interest rates (which can be approximated by the US Treasury bond term structure) and the term structure of risk premiums at time, t , and t  1 , the news terms, NRF and NRP , can be obtained. Observing the stock market’s return from t to t  1 , cash-flow news, NCF , are NCFt  URt  NRFt  NRPt . Before presenting empirical results in the following section, we believe it necessary to discuss potential limitations of our approach. These limitations can be characterized by (i) empirical issues such as data restrictions and (ii) assumptions on the preference function, which are necessary to transform a risk-neutral PDF into a real PDF using Equation (8). The first limitation refers to option data, which are available only for a limited set of maturities, T (e.g., two years), and for a limited set of exercise prices, denoted by K . Thus, one must make additional assumptions pertaining to how the PDFs are derived for long maturities and large as well as low exercise prices for which no option prices are available. In addition, one must discretize the continuous approach described earlier as exercise prices are not available on a continuum. These assumptions are described in Appendix A. It should be noted that the assumptions necessary for discretizing and extending the limited T  K space have only a minor impact on the empirical results presented in the next section. The second limitation arises from the assumption on the utility function. We consider the second limitation by employing different risk-aversion coefficients,  , in our robustness section. Further, we change the power utility function to a habit utility

9

function (Campbell and Cochrane, 1999), thereby allowing for time-varying risk aversion. This section shows that empirical results and conclusions are rather robust with respect to the second issue.

3 Empirical results 3.1 Data and assumptions on investor’s preferences Our sample covers the period from January 1997 to December 2017. We used daily prices of S&P 500 index options (European style) from OptionMetrics (provided by Wharton Research Data Services) before 2008 and Bloomberg data thereafter. The empirical implementation of the OIR approach leverages options with maturities of 1, 3, 6, 9, 12, 18, and 24 months. We obtain dates of a-days of FOMC meetings from the website of the FED. We measure recession and expansion periods using the NBER’s recession definition. Yields of US Treasuries are obtained from the Federal Reserve Economic Data (FRED) database. We set the risk-aversion parameter in Equation (7) to   2 , which implies a median one-year expected equity return of approximately 8.9%. Subtracting the average one-year interest rate of 3.2% for US government bonds yields an average one-year equity premium of 5.7%, which is approximately the excess return of the US stock market over the sample period. In the robustness section 4, we vary this assumption to  {1,5} in order to analyze the sensitivity of empirical results. Although these alternative assumptions on the risk-aversion parameter yield risk premiums which are difficult to justify empirically, the main results are rather robust to those alternatives. We further change the power utility function to habit utility. Again, the results are robust to this change.

3.2 Descriptive statistics: Cash-flow news and discount rate news on a-days and n-days Table 1 summarizes descriptive statistics for the US stock return (S&P 500 index) on a-days and n-days, both unconditional and conditional upon expansion and recession periods. On a-days, the S&P index earns an average return of 35.05 bps (column (1)), while the average return on n-days is just 2.07 bps (column (2)). This result confirms the studies of Savor and Wilson (2013) and Lucca and Moench

10

(2015), who showed that the average return is substantially larger on a-days of major economic news and, in particular, on FOMC a-days than it is on n-days. Considering that the number of n-days is roughly 30-fold larger than the number of a-days (5306 vs. 166), the cumulative return conditional upon the sets of a-days and n-days is worth mentioning, which is only two-fold larger for n-days compared to a-days. This observation highlights the importance of FOMC announcement days for the stock market performance over the sample period. TABLE 1 Descriptive statistics for daily returns on the S&P 500 and decomposed returns All days N

Expansion days

Recession days

a-days

n-days

a-days

n-days

a-days

n-days

166

5306

145

4762

21

544

(1)

(2)

(3)

(4)

(5)

(6)

Return (R) Mean

35.05

2.07

27.57

3.62

86.70

–11.43

t-stat

3.34

1.28

2.90

2.44

1.72

–1.26

135.35

118.29

114.44

102.13

231.60

212.23

5,818.10

10,999.78

3,997.33

17,219.79

1,820.77

–6220.01

Std cumret

Expected return (ER) Mean

3.75

3.54

3.19

3.13

7.59

7.14

t-stat

16.80

97.81

19.75

119.26

7.24

33.52

2.87

2.64

1.94

1.81

4.80

4.97

621.83

18,776.93

462.35

14,893.33

159.48

3,883.60

Std cumret

Unexpected return (UR) Mean

31.30

–1.47

24.38

0.49

79.11

–18.57

t-stat

2.99

–0.90

2.57

0.33

1.57

–2.04

134.79

118.22

114.05

102.05

231.28

211.90

5,196.28

–7,777.14

3,534.98

2,326.46

1,661.29

–10,103.61

Std cumret

Cash-flow news (NCF) Mean

10.29

–0.83

6.67

1.14

36.35

–18.28

t-stat

1.18

–0.54

0.77

0.75

1.05

–2.61

112.53

112.36

104.82

104.91

158.54

163.50

1,688.06

–4,218.25

961.10

5,214.42

726.96

–9,432.67

Std cumret

Interest rate news (–NRF) Mean

1.74

1.00

2.64

0.95

–4.47

1.44

t-stat

0.25

0.99

0.41

0.94

–0.14

0.32

89.30

73.72

77.56

69.41

149.77

104.20

288.37

5,296.00

382.27

4,513.36

–93.91

782.64

72.41

–3.94

Std cumret

Risk premium news (–NRP) Mean t-stat Std

22.37

–1.66

15.42

–1.40

2.42

–0.84

1.66

–0.72

2.14

–0.43

119.05

144.25

112.11

134.28

154.87

213.49

11

cumret

3,668.27

–8,469.27

2,220.05

–6,434.29

1,448.22

–2,034.98

The expected return does not seem be able to explain the difference as the expected return on adays is just marginally greater than on n-days (3.75 bps vs 3.54 bps). As a consequence, the average unexpected return is large on a-days (31.30 bps) and almost zero on n-days (–1.47 bps). It should be noted that we approximate the expected daily return from option prices with a one-month maturity. If option prices with a maturity of one day were available, an alternative expected daily return could potentially be obtained, although it is unlikely that it could explain the large size of the unexpected return. Indeed, the cumulative unexpected return on a-days is plus 5,196 bps versus minus 7,777 bps on n-days. The unexpected return over all a-days and over all n-days are of the same order, indicating that the OIR is equivalent to the realized return over the total sample period quite accurately, which is the result of setting the risk-aversion parameter to  = 2. With respect to the three news factors, NCF, NRF, and NRP, the majority of the unexpected return on a-days can be attributed to risk premium news. Approximately two thirds of the high average unexpected return on a-days (31.30 bps) is explained with risk premium news (22.37 bps). In other words, the large unexpected stock market return on a-days is driven by an unexpected fall in the risk premium. This observation provides a first indication of the importance of the risk premium channel of MP. Please note that the cumulative risk premium news on a-days is positive (3,668 bps) while it is negative on n-days (–8,469 bps). Thus, the risk premium seems to fall sharply on a-days while it gradually rises on n-days. The separation of announcement days into expansion and recession periods (columns (3) and (5)) exemplifies the business cycle properties of the stock return components. During a recession, the return on an a-day is about three times higher than during an expansion period (87 bps vs. 28 bps, respectively). The higher return is accompanied by a greater standard deviation on a recession a-day compared to an expansion a-day (232 bps vs. 114 bps, respectively). The expected return – although higher during a recession (7.59 bps) than during an expansion (3.19 bps) – may help to explain this large difference in realized returns only partially. Therefore, the unexpected part of the realized average return is still large and can be mainly attributed to risk premium news. Hence, the risk premium channel seems to be the

12

most important for explaining the unexpected return, primarily on a recession a-day. Risk premium news accounts for 72 bps of the average unexpected return (of 79 bps) on a typical recession a-day. Non-announcement days have a considerably lower average return of 4 bps during expansions and minus 12 bps during recessions (columns (4) and (6)) compared with a-days. As the expected return is more than two-fold larger during recession periods than expansion periods (7.14 bps versus 3.13 bps, respectively), the cumulative unexpected return is negative over recession periods (–10,104 bps) and positive over expansion periods (2,326 bps). These cumulative unexpected returns can thereby be primarily understood via cash-flow news. That is, during expansions, cash-flow expectations are revised upwards while during recession periods, they are revised downwards. Interest rate news contributes positively to the unexpected stock returns on n-days during expansions (that is, on average, interest rate surprises are positive) but are compensated by risk premium news, which are negative on n-days (that is, risk premium rises unexpectedly). In addition, on n-days, risk premium news is also negative during recessions. Thus, the news component of the risk premium is not systematically related to the business cycle but seems to be systematically associated with the announcement calendar of the FED. To sum up, the main driver of the unexpected return on a-days seems to be risk premium news while on n-days, it is mainly cash-flow news that drives the unexpected return. The risk premium falls unexpectedly on a-days, particularly strongly on a recession a-day. Additionally, cash-flow news is economically plausible because cash-flow expectations rise during expansion periods and fall during recessions. The OIR approach therefore delivers estimates on expected returns and the three news components, which are all economically plausible. While the descriptive statistics highlights the importance of the risk premium channel, they do not address the issue of how surprises in MP decisions are related to unexpected stock returns and their three components. We address this issue in the next section.

3.3 Monetary policy effects on stock returns The descriptive analysis implies that the risk premium channel of MP seems to play an important role when investigating the relation between stock prices and monetary policy. On a-days, however, the

13

previous analyses do not show how monetary policy is actually working through the risk premium channel. That is, does a surprise in monetary policy lead to a lower (higher) risk premium? This question is often answered in an unconditional setting by assuming that regression parameters are constant in different economic states (see in equation (5)). However, the impact of monetary policy on stock returns and their components can vary over the business cycle (e.g., Basistha and Kurov, 2008).5 The descriptive statistics displayed in Table 1 support such a dependence. We therefore introduce a dummy variable, Dt , which equals one in the economic state ‘recession’ and zero in the state ‘expansion’:

A t  A  Dt  A rec , (10)

Bt  B  Dt  B . rec

Replacing the regression parameters in equation (5) with (11) yields:

N t  A  Dt  A rec  B  NMPt  Dt  B rec  NMPt  Εt .

(11)

In Equation (11), B characterizes the MP-SR in expansions and B  B rec in recessions. Table 2 summarizes the parameter estimates of various specifications of the MP-SR and its decomposition. Consistent with previous research, the table shows in row (1) that the slope parameter is estimated to be smaller than zero at –2.26 in the unconditional specification (no recession dummy). This is somewhat smaller than earlier studies have reported, but the smaller slope can be explained by the recent years of the sample period. If we use, for example, a restricted sample ending in December 2002, which is the end date in the Bernanke and Kuttner (2005) study, the slope is estimated at –8.73.6

There are several economic explanations for such a state dependence. For example, according to the balance sheet channel (Fazzari et al., 1988; Bernanke and Gertler, 1989), balance sheets and the value of collaterals in recessions are usually in a worse condition than during expansions. This makes the financing of new (and existing) projects costlier (i.e., a higher risk premium) and more sensitive to monetary policy surprises during recessions than expansions. As such, a change in monetary policy may have a different impact on stock prices in recessions than expansions. 6 Estimates and their significance levels vary considerably in the literature depending on the sample period and method. For example, Chulia et al. (2010) reported a slope of almost –10 while Kontonikas et al. (2013) described a slope of just –2 while Bernanke and Kuttner reported a slope of roughly –4. With respect to individual stocks, there is also a large heterogeneity (e.g., Ehrmann and Fratzscher, 2004). . 5

14

Over the full sample, an unexpected decrease in the interest rate of 100 bps is followed by a 226 bps rise in the stock price, although the point estimate is only significant at the 10% level. Looking at the unexpected return regression (row (2)), the slope is estimated less negatively (– 2.19), although the difference from the raw return regression is rather small. The small difference in the slopes in row (1) and (2) can be explained by the well-known fact that expected returns for a daily horizon are rather small compared to the realized return. The decomposition of the MP-SR (rows (3a) to (3c)) reveals that a large part of the negative slope can be attributed to cash-flow news (the estimated slope, b NCF , equals –3.23 in row (3a) with a p-value of less than 1%). The slopes on NRF and NDR, however, are not significant. It is necessary to remember that the slope parameter in the OLS regression using the unexpected return as the dependent variable is equivalent to the sum of slopes on NCF, NRF and NRP in the SUR regression, b NCF  b  NRF  b  NRP  bUR . Thus, in economic terms, the cash-flow channel of monetary policy has the largest and most significant effect in the unconditional specification. As a consequence, the negative parameter is consistent with a “controlling channel” of MP. Unexpectedly higher interest rates lead to lower cash-flow expectations and finally lower inflation expectations, which may be the target of central bankers when they raise interest rates in a booming economy to fight against inflationary pressure (i.e., inflation targeting). On the other hand, a negative slope parameter, b NCF , also suggests that lower-than-expected interest rates are accompanied by rising cash-flow expectations. This relation is also economically reasonable as falling interest rates make financing conditions cheaper, which finally might result in higher earnings. TABLE 2 Regression estimates of returns. unexpected returns and their components based on monetary policy news on announcement days of FOMC meetings

Rt 1  a  b  NMPt 1   t 1 , specifications (1) and (4)

URt 1  aUR  bUR  NMPt 1   t 1 , specifications (2) and (5) N t  A  Dt  A rec  B  NMPt  Dt  B rec  NMPt  Εt , specifications (3a-c) and (6a-c) a b a rec b rec

adj R2

OLS regression (1) R (2)

UR

SUR regression (3a) NCF

0.356 *** 0.001 0.320 *** 0.002

–2.257 * 0.069 –2.192 * 0.076

0.014

0.062 0.473

–3.226 *** 0.002

0.023

0.013

15

(3b)

–NRF

0.017 0.811 0.241 ** 0.011

–0.319 0.709 1.353 0.234

(3c)

–NRP

0.246 ** 0.016 0.214 ** 0.036

–9.048 *** 0.000 –9.007 *** 0.000

1.047 *** 0.001 1.002 *** 0.001

10.717 *** 0.000 10.676 *** 0.000

0.123

0.030 –10.719 *** 0.729 0.000 (6b) –NRF 0.033 2.556 0.654 0.132 (6c) –NRP 0.151 –0.843 0.117 0.702 ***,**,* denotes significance at the 1%, 5%, and 10% levels

0.313 0.237 –0.156 0.491 0.846 *** 0.005

10.456 *** 0.000 –4.070 ** 0.042 4.289 * 0.099

0.086

OLS regression (4) R (5)

UR

SUR regression (6a) NCF

0.119

The inclusion of a recession dummy (specifications (4) to (6)) demonstrates that MP-SR is different during expansion and recession periods. In the unexpected return regression (row (5)), the expansion slope, bUR , is estimated to be even more negative (approximately –9.01) while the recession dummy, bUR ,rec , is significantly positive (about 10.68). This implies that an unexpected reduction in interest rates on a-days is accompanied by higher stock returns during an expansion period and slightly lower stock returns in recessions ( bUR  bUR ,rec = –9.01 + 10.68 = 1.67). Therefore, the decomposition of the slope parameters as given by the SUR coefficients (rows (6a-c)) reveals that during expansion periods, the “controlling channel” seems to be the dominant characteristic of the MP-SR. In recessions, however, this channel is no longer effective as the slope is significantly larger in recessions than in expansion periods. In particular, the recession NCF slope is estimated to be b NCF  b NCF ,rec = –10.72 + 10.46 = –0.26. On the other hand, interest rate news and risk premium news seem to become more important in recessions (although with different signs). Their slope dummies ( b  NRF ,rec and b  NRP , rec ) are significant (at least at the 10% level), suggesting that the MP-SR varies in recessions. Yet, how can the MP-SR in a recession be characterized? The recession slope in the NRF regression (

b  NRF  b  NRF ,rec = 2.56 – 4.07 = –1.51) shows that lower FED fund futures rates support stock prices via lower interest rates. However, they are also accompanied by higher risk premiums ( b  NRP  b  NRP ,rec = –0.84 + 4.29 = 3.45), which finally leads to higher discount rates and lower stock prices. Thus, an

16

unexpected expansionary MP instrument during a recession period results in higher risk premiums and unchanged cash-flow expectations. Such a MP-SR characteristic is consistent with the view that the FED’s MP decisions is interpreted by market participants as a signal that the economy is in a worse than expected condition. We interpret the decomposed MP-SR as a “signaling channel”. However, the sole consideration of the slope does not fully characterize the MP-SR as the recession intercept is positive and highly significant ( aUR  aUR ,rec = 0.214 + 1.002 = 1.216). Independent of the decision being announced, the stock market rises unexpectedly by 122 bps. A large part of this stock increase can be attributed to a fall in the risk premium ( a  NRP  a  NRP ,rec = 0.151 + 0.846 = 0.997). Hence, the large and positive intercept in recessions may reflect that investors are confident that the central bank provides certain downside protection for stock holders. Such downside protection, for example, could be a renewed confidence in the FED’s ability to shorten the duration of a potential economic downturn or prevent an acceleration of the recession. As downside protection is a non-mandatory insurance pledge of the FED that may be restated or withdrawn on a-days, thereby introducing some policy risk, investors may value it independently from the particular monetary policy chosen. Such an insurance effect is often termed “Fed put” (originally known as the “Greenspan put”). We, therefore, characterize the positive intercept in the recession MP-SR as a “risk channel” seeing that risk premium are the main driver of a-day stock returns. In sum, the MP-SR is different during expansions and recessions. On expansion a-days, the size of unexpected MP decisions has a significant impact on cash-flow expectations, indicating that monetary policy is perceived as being able to control the growth rate of the economy (“controlling channel”). On recession a-days, however, we observe a different pattern, which we characterize as a “signaling channel” and a “risk channel” of MP. Additionally, the adjusted R2 of the UR regression, including a recession dummy (11.9%), is substantially larger than that without it (1.3%). Thus, allowing constants and slopes to vary in economic states enhances the explanation power of the MP-SR substantially and offers a more detailed interpretation of how MP works. We are not the first to link MP surprises to decomposed stock returns. However, to the best of our knowledge, we are the first to do so on a daily basis with a focus on days when MP is announced.

17

Bernanke and Kuttner (2005) addressed this issue for monthly US stock returns and, thereby, analyze medium-term effects of MP decisions. They used a predictive regression approach for the expected return in a VAR context following Campbell and Ammer (1993).7 Their results suggest that an unexpected fall in interest rates during a month increases dividend expectations (which is compatible with a-days regression slopes and the controlling effect) and lowers the future risk premium, where risk premium news explains the largest part of the unexpected return. Bernanke and Kuttner, however, employ a monthly VAR and therefore decompose monthly returns. Monthly returns then also encompass n-days. We, therefore, report parameter estimates of the MP-SR observed on n-days in Table 3. It should be noted that MP news estimated from unexpected changes in federal funds futures on n-days reflect the perception of market participants regarding how the FED will react to incoming information. Table 3 shows that the MP-SR on n-days varies from that on a-days in two main respects. First, the slope parameter is positive indicating that a looser perceived MP is associated with lower stock returns. The positive slope is compatible with the signaling channel. In the unexpected return regression, the slope, bUR , equals 6.66, which can be positively attributed to cash-flow revisions ( b NCF  3.95) and risk premium news ( b  NRP  9.61) and negatively to interest rate news ( b  NRP  –6.90). Thus, an unexpected drop in federal funds futures on n-days is associated with a decrease in cash-flow expectations and increase in the equity risk premium. This pattern is the same when expansion and recession slopes are estimated separately, although during recessions, the slopes are larger. Second, intercepts are generally not significantly positive on n-days, which is also in contrast with a-days regressions. If at all, they are negative on recession n-days. We have previously interpreted the positive a-days intercept (in recessions) as a risk channel that may characterize non-mandatory downside protection in recessions. The negative intercept on n-days is also in line with this view as on n-days, such a non-mandatory pledge cannot be renewed. These two observations may serve as additional justification to separate a-days and n-days when the MP-SR is characterized. Employing monthly return frequencies, however, may hide a proportion of the announcement effects of MP as a monthly frequency mixes a-days and n-days.

It should be noted that results in this study cannot be directly compared with that of Bernanke and Kuttner (2005) because of different sample periods and econometric approaches. 7

18

TABLE 3 Regression estimates of returns. unexpected returns and their components based on monetary policy news on nonannouncement days (i.e., trading days without announcements from FOMC meetings)

Rt 1  a  b  NMPt 1   t 1 , specifications (1) and (4)

URt 1  aUR  bUR  NMPt 1   t 1 , specifications (2) and (5) N t  A  Dt  A rec  B  NMPt  Dt  B rec  NMPt  Εt , specifications (3a-c) and (6a-c) a b a rec b rec

adj R2

OLS regression (1) R (2)

UR

SUR regression (3a) NCF (3b)

–NRF

(3c)

–NRP

OLS regression (4) R

0.022 0.201 –0.013 0.434

6.550 *** 0.000 6.658 *** 0.000

0.019

–0.008 0.632 –0.003 0.797 –0.003 0.885

3.954 *** 0.000 –6.902 *** 0.000 9.607 *** 0.000

0.020

4.707 *** 0.000 4.754 *** 0.000

–0.119 ** 0.033 –0.159 *** 0.004

4.200 *** 0.002 4.249 *** 0.002

0.022

0.009 3.217 *** 0.603 0.000 (6b) –NRF 0.002 –7.612 *** 0.890 0.000 (6c) –NRP –0.006 9.149 *** 0.782 0.000 ***,**,* denotes significance at the 1%, 5%, and 10% level

–0.154 *** 0.003 –0.037 0.286 0.032 0.630

1.409 0.270 1.639 * 0.052 1.201 0.465

0.023

(5)

UR

0.035 ** 0.049 0.004 0.810

0.020

SUR regression (6a) NCF

0.023

4 Robustness checks 4.1 Alternative assumptions on investors utility A potential weakness of the OIR approach, which we utilized to identify cash-flow and discount rate news, is the assumption surrounding investors’ preferences. The previous section assumed a power utility investor with a risk-aversion coefficient of   2 . Although this assumption has been justified economically (it yields a median expected stock return of about 9% and a risk premium of slightly less than 6% per annum, which approximately equals the average excess return over the sample period), it may not describe investor’s preferences correctly. In this section, we therefore evaluate alternative riskaversion parameters, i.e.,  1, 5 , to verify whether empirical results and implications for the MP-

19

SR change substantially. In general, a lower risk-aversion coefficient implies a lower estimate of the expected stock return and vice versa. In particular, the median one-year expected stock return is equivalent to 5.4% (   1 ) and 17.5% (   5 ), respectively. A further increase in risk aversion yields an even higher median expected return. For example, employing   10 yields an unrealistically high median one-year expected return of 29.9%. Additionally, we consider an alternative utility function suggested by Campbell and Cochrane (1999). They model preferences according to a habit utility function. To be specific, consumers value their consumption relative to a slow-moving external habit, producing a countercyclical variation in discount rates. Then, preferences are assumed to be characterized by the following utility function:

U (C , X ) 

 C  X 1 1 

.

(12)

where X is the external habit level. This habit level can be calculated as follows (e.g., Li, 2001):

 1   m  J  j 1 m X t 1      Ct  j ,  1   Jm  j 1

(13)

 is the persistence parameter set to 0.98 (using quarterly consumption data), J  1 is the duration of habit (setting to 20 quarters), and  is a coefficient that controls the habit level regarding current consumption. Replacing the power utility function (7) by the habit utility function (12) in the OIR approach, the real PDF is obtained as (for a detailed derivation, see Appendix B):  ST  CSRT   ft * ( ST )  ft ( ST )  ,  * x  CSR  f ( x ) dx   t t 

(14)

where CSRt   Ct  X t  Ct is the consumption surplus ratio. Similar to equation (9), the OIR can be derived according to the PDF in (14). Table 4 summarizes the estimates of the SUR coefficients. In general, we obtain similar results and can, therefore, draw the same conclusion as in our base case assumption on investor preferences (power utility with  = 2): The MP-SR decomposition is compatible with a controlling channel in

20

expansion periods and with a signaling channel and risk channel during recession periods across various assumptions about investors’ preferences. That is, lower-than-expected interest rates are followed by higher (flat) cash-flow expectations during expansions (recessions). Moreover, in recessions, the risk premium falls unexpectedly independently from the MP being announced, but the fall in the risk premium is lower if an unexpected fall in interest rates is announced. Overall, the characterization of the MP-SR is similar across different assumptions on investor preferences. TABLE 4 Regression estimates of returns. unexpected returns and their components based on monetary policy news on announcement days of FOMC meetings using alternative assumptions on investor preferences

Rt 1  a  b  NMPt 1   t 1 , specifications (1) and (4)

URt 1  aUR  bUR  NMPt 1   t 1 , specifications (2) and (5) N t  A  Dt  A rec  B  NMPt  Dt  B rec  NMPt  Εt , specifications (3a-c) and (6a-c) a b a rec b rec

adj R2

Panel A: Power utility, =1 NCF

–10.542 *** 0.000 2.556 0.132 –1.027 0.690

0.749 *** 0.009 –0.156 0.491 0.427 0.216

11.076 *** 0.000 –4.070 ** 0.042 3.679 0.225

0.077

0.078 –11.085 *** 0.670 0.009 –NRF 0.033 2.556 0.654 0.132 –NRP 0.075 –0.446 0.648 0.906 Panel C: Power utility with habit, time varying risk aversion NCF 0.005 -10.315 *** 0.953 0.000 –NRF 0.033 2.555 0.652 0.133 –NRP 0.066 –1.215 0.488 0.579 ***,**,* denotes significance at the 1%, 5%, and 10% level

–0.879 0.121 –0.156 0.491 1.988 *** 0.000

8.071 * 0.095 –4.070 ** 0.042 6.642 0.136

0.079

0.499 * 0.079 –0.156 0.491 0.590 ** 0.045

10.513 *** 0.000 –4.070 ** 0.042 4.187 * 0.095

0.072

–NRF –NRP

0.031 0.742 0.033 0.654 0.167 0.138

Panel B: Power utility,  =5 NCF

4.2 Subperiod analysis: Unconventional monetary policy The federal funds rate approached almost zero from December 2008 onwards and the FED changed its policy function to what it called “unconventional monetary policy”. At least two additional instruments were implemented: First, a large-scale asset purchase program aimed at lowering long-term interest rates. Second, the promise to keep short-term interest rates close to zero for a long period of

21

time provided information about the path of interest rate policy (extension of zero investment policy (ZIRP)). Employing these instruments to set monetary policy, unexpected changes in federal funds futures (which we use as a proxy for the NMP) may not fully capture MP news. To measure unconventional MP instruments, we followed Hanson and Stein (2015) who suggested making use of changes in the two-year US government bond yield as a proxy for news in MP which we orthogonalized to the news components obtained from federal fund futures.8 We run regressions (11) with these zirp

alternatives, and included a dummy, Dt

, which equals one during the ZIRP period:9

A t  A  Dtrec  A  Dtzirp  A,

(15)

Bt  B  Dtrec  B  Dtzirp  B.

Replacing the regression parameters in equation (5) with (15) and using two dimensions of MP news fff (derived from federal funds futures, denoted by NMPt , and from two-year treasury bond yields, 2y denoted by NMPt ) yields:

N t  A  Dtrec  A rec  Dtzirp  A zirp

  B

   NMP

 B fff  Dtrec  B rec , fff  Dtzirp  B zirp , fff  NMPt fff 2y

 Dtrec  B rec ,2 y  Dtzirp  B zirp ,2 y

2y t

(16)

 Εt .

Table 5 presents the results of applying equation (16), and we obtain four main results. First, the explanatory power is substantially greater in the SUR system, which includes two-year yield changes and a ZIRP dummy, than in a system without the two variables (system R2 of 36% compared to 8% as in Tables 3 and 4). Thus, changes in the two-year bond yields seem to contain additional information on how stock prices are related to MP news. Second, looking at the intercepts of the regressions (first three columns) confirms the previous result that the recession intercept in the UR regression is large (0.827) and can be mainly explained by

Accordingly, Kontonikas et al. (2013) have shown that the stock market response to unexpected changes in the federal funds futures is different during times before and after 2008. Also, Gagnon et al. (2011) and Hamilton and Wu (2012) documented that unconventional MP instruments had a significant impact on bond yields. Therefore, employing changes in two-year bonds seems to be an adequate proxy for unconventional MP instruments. 9 On December 16, 2008, the FED decided to establish a target range for the federal funds rate of 0 to 0.25%. On December 16, 2015, the FED changed the target rate to 0.25 to 0.5%. The time period between the two decisions is known as zero interest-rate policy (ZIRP). 8

22

risk premium news (0.790). In addition, with the NRP regression, the ZIRP intercept is also significantly positive (0.357). Thus, during the ZIRP period, the fall in risk premiums on a-days of MP – independently from the policy being announced – was particularly large. If we interpret the intercept as the result of the FED’s pledge to provide a modicum of downside protection, this insurance effect seems to be particularly valuable during ZIRP. The significant negative intercept in the NRF regression, however, dampens the corresponding rise in stock prices resulting from falling risk premiums. As a result, with the UR regression, the ZIRP intercept is small and not significant. In sum, the risk premium channel seems to be an important characteristic of the MP-SR during the ZIRP period. TABLE 5 Regression estimates of returns. unexpected returns and their components based on monetary policy news

N t  A  Dtrec  A rec  Dtzirp  A zirp

  B

   NMP

 B fff  Dtrec  B rec , fff  Dtzirp  B zirp , fff  NMPt fff 2y

 Dtrec  B rec ,2 y  Dtzirp  B zirp ,2 y

a R UR NCF –NRF –NRP

arec

2y t

azirp

bfff

 Εt .

brec,fff

bzirp,fff

b2y

brec,2y

bzirp,2y

0.896

1.097

–4.721

0.611

0.754

0.221

0.874

0.988

–4.591

0.045

0.620

0.777

0.233

0.213 *

0.864 ***

0.076

–8.451

0.086

0.007

0.707

0.000

0.179

0.827 **

0.083

–8.432

0.149

0.010

0.681

0.000

0.048

0.253

–0.043

0.640

0.344

0.801

0.099

–0.216

0.106

0.170

0.022

0.167

0.091 *

0.031

0.790 ***

0.357 **

0.146

2.654

–7.513

0.777

0.006

0.049

0.945

0.285

0.383

–0.231 **

***

9.968 *** 0.000

***

–10.186 ***

9.957 *** 0.000 9.627 ***

–20.069 ** 0.039 –19.423 ** –6.556

2.134

2.071

2.095

0.000

0.000

0.417

0.150

0.480

0.516

1.607

–2.324

–5.354 0.262

–6.447 ***

-2.498

–9.208 ***

0.000

0.149

0.000

5.187 ***

1.415

2.522

0.001

0.650

0.463

Third, the ZIRP slope on MP news from federal funds futures is significantly negative in the UR regression, where the MP-SR adds to b fff  b zirp , fff = –8.432 – 19.423 = –27.855. A MP surprise of –10 bps as measured by federal funds futures is followed a positive stock market return of 2.79%. This relation is larger than previously reported (consider that the slope in Bernanke and Kuttner (2005) equals roughly 4). However, it should be noted that the unexpected changes measured by the federal funds futures are substantially lower in ZIRP than outside ZIRP, i.e., the standard deviation of a-day changes in federal funds futures is 0.0182 (in ZIRP) and 0.0999 (outside ZIRP), see also Kiley (2014; Figure 1). Therefore, surprises in MP as measured by federal funds futures are rather small, which illustrates to some extent the size of the slope coefficient. Looking at the slope coefficients in the UR regression and its decomposition further suggests that all news components contribute almost equally to the negative

23

adj R2 0.141 0.134 0.361

UR-NMP relation ( b zirp , fff  b zirp , fff , NCF  b zirp , fff , NRF  b zirp , fff , NRP  6.556  5.354  7.513 ). All in all, the MP-SR during ZIRP seems to be more pronounced as indicated by large slopes. Fourth, the slope on the alternative NMP measure, two-year yield changes, is also negative in the ZIRP period, b 2 y  b zirp ,2 y = 0.874 – 4.591 = –3.717, but it is rather imprecisely estimated. The negative slope suggests that non-conventional MP decisions further strengthens the previously documented negative SR-MP relation from using federal funds futures to approximate NMP. Therefore, the decomposed

slope

( b zirp ,2 y  b zirp ,2 y , NCF  b zirp ,2 y , NRF  b zirp ,2 y , NRP

 2.095  9.208  2.522  4.591 ) reveals that, in particular, the interest rate news component contributes most to the negative ZIRP slope dummy. Ultimately, conventional MP instruments in expansion periods operate through a different channel (i.e., cash-flow expectations) than unconventional instruments (i.e., risk premium channel). In the previous section, we interpreted a negative slope during expansion periods, which is primarily explained by cash-flow news, as a controlling channel. That is, the central bank may control the growth rate of the economy by setting short-term interest rates to which investors adjust their cash-flow expectations (i.e., growth expectations). During ZIRPs, the controlling channel is still observable and additionally supplemented by the risk premium channel (significant ZIRP intercept). Furthermore, the ZIRP slopes are primarily explained by risk-free rate news (negatively) and risk premium news (positively). Thus, an unexpected fall that is signaled by unconventional instruments leads to higher risk premiums, which may also offer support to the signaling effect. That is, through looser MP, the central bank may signal that the economy is in worse condition than expected and during ZIRP, the MP news may have been better captured by changes in the two-year bond yield. During recessions and also during ZIRP, the risk premium channel has become more important. This interpretation is also compatible with the “risk-taking effect” of Borio and Zhou (2012), which characterizes the MP as supporting banks and investors taking on more risky assets.10 However, as prices of risky assets, such as stocks, rise mainly

A risk-taking effect of MP has been documented for other markets, e.g., the credit market (Dell’Ariccia et al., 2017), the bond market (Becker and Ivashina, 2015), and the market for money market funds (Di Maggio and Kacperczyk, 2017). These studies, however, do not analyze the announcement effect of MP decisions directly, but the long-term trends in the supply and demand of high yielding (and therefore high-risk) securities. 10

24

through falling risk premiums, the corresponding wealth effect of MP may be just temporary. As such, the long-term effects of the risk premium channel may be disappointing as if a higher wealth today also leads to a higher consumption today, lower risk premiums (and lower future returns) in the future may lower future consumption growth. That is, a greater current consumption “borrows” from future consumption. With this, the main conclusion from the decomposition exercise of a-day stock returns is that a main channel through which MP news functions underwent a change during the financial crisis in 2008 and the risk premium channel became more important.

5. Conclusion The analysis within this paper shows that stock prices respond to MP surprises differently over time. On average, an unexpected fall in short-term interest rates corresponds to a rise in stock prices. The response of stock prices to MP news is, however, different in two respects. First, a stock market increase following lower interest rates is primarily observed during time periods when the economy is in an expansion state. During recessions, stock prices rise independently of the interest decision being made. Then, the rise is smaller when interest rate surprises are negative. Second, a decomposition of the daily stock market returns when MP is announced into cash-flow news, interest rate news, and risk premium news gives the stock market’s response coefficient to MP news a more detailed economic interpretation. This decomposition exercise reveals that stock prices respond to MP surprises during recessions and expansions differently. During expansions, an unexpected fall in interest rates of 25 bps is followed by a rise in cash-flow expectations, leading to higher stock prices of 268 bps. During recessions, however, a positive stock return of 124 bps is observed independent from the interest decision being announced on that day. If, additionally, an unexpected fall in interest rates of 25 bps is announced, the stock market rise is lowered by 42 bps, which can be explained primarily by higher risk premiums. Thus, stock market investors interpret MP news differently over the economic cycle. On the basis of the decomposition approach of the stock market’s response coefficient to MP news, we characterize the stock market’s reaction to interest rate surprises during expansions as if MP

25

is able to control the growth rate of the economy (i.e., controlling channel). Lower interest rates then elevate growth expectations, leading to higher cash-flow expectations. During recessions, however, lower interest rates may be interpreted by stock market investors as a signal from MP makers such that the economy is performing less well than expected (signaling channel), resulting in higher risk premiums. Risk premium news further imply a substantial stock market increase independent from the interest rate surprise component. This rise is thereby substantially larger during recessions than expansions. This observation characterizes the investors’ perception of how MP makers may respond to a recession. They seem to provide downside protection (i.e., FED put) for stock market investors in the case of interest rate decisions. As this protection is a non-mandatory pledge that leads to lower risk premiums and rising stock markets independent from the interest rate decision when it is renewed on an announcement day, we characterize this channel as a risk premium channel, which appears to have strengthened during the recession following the financial crisis of 2008. Overall, the decomposition of announcement day returns helps determine the effects of MP decisions in more detail. The importance of risk premium news, especially during recessions and after the financial crisis in 2008, supports the view that the risk premium channel of MP (risk-taking effect and search-for-yield effect) is important. This has a direct impact on the wealth channel of MP. If the relation between the stock market and MP is predominantly driven by risk premium news, the effects on wealth and finally consumption may only be temporary as a higher wealth today brought about by a falling risk premium implies a smaller growth rate of future wealth and also future consumption.

26

References Ait-Sahalia, Y., Lo, A.W., 2000. Nonparametric risk management and implied risk aversion. Journal of Econometrics, 94, 9–51. Ando, A., Modigliani, F., 1963. The “life cycle” hypothesis of saving: Aggregate implications and tests. American Economic Review, 53, 55–84. Basistha, A., Kurov, A., 2008. Macroeconomic cycles and the stock market’s reaction to monetary policy. Journal of Banking and Finance, 32, 2606–2616. Becker, B., Ivashina, V., 2015. Reaching for yield in the bond market. Journal of Finance 70, 1863– 1901. Bernanke, B., Gertler, M., 1989. Agency costs, net worth, and business fluctuations. American Economic Review, 79, 14–31. Bernanke, B., Kuttner, K., 2005. What explains the stock market’s reaction to Federal Reserve policy? Journal of Finance, 60, 1221–1256. Black, F., Scholes, M., 1973. The pricing of options and corporate liability Journal of Political Economy, 81, 637–654. Borio, C., Zhu, H., 2012. Capital regulation, risk-taking and monetary policy: A missing link in the transmission mechanism? Journal of Financial Stability, 8, 236–251. Campbell, J.Y., 1991. A variance decomposition for stock returns. Economic Journal, 101, 157–179. Campbell, J.Y., Ammer, J., 1993. What moves the stock and bond markets? A variance decomposition for long-term asset returns. Journal of Finance, 48, 3–37. Campbell, J.Y., Cochrane, J.H., 1999. By force habit: A consumption-based explanation of aggregate stock market behavior. Journal of Political Economy, 107, 205–251. Campbell, J.Y., Shiller, R.J., 1988. Stock prices, earnings, and expected dividends. Journal of Finance, 43, 661–676.

27

Cox, J.C., Ross, S.A., 1976a. A survey of some new results in financial option pricing theory. Journal of Finance, 31, 383–402. Cox, J.C., Ross, S.A., 1976b. The valuation of options for alternative stochastic processes. Journal of Financial Economics, 3, 145–166. Chuliá, H., Martens, M. van Dijk, D., 2010. Asymmetric effects of federal funds target rate changes on S&P100 stock returns, volatilities and correlations. Journal of Banking and Finance, 34, 834–839. Dell’Ariccia, G., Laeven, L., Suarez, G.A., 2017. Bank leverage and monetary policy’s risk-taking channel: Evidence from the United States. Journal of Finance, 72, 613–654. Di Maggio, M., Kacperczyk, M., 2017. The unintended consequences of the zero lower bound policy.” Journal of Financial Economic, 123, 59–80. Dumas, B., Fleming, J., Whaley, R.E., 1998. Implied volatility functions: Empirical tests. Journal of Finance, 53, 2059–2106. Fazzari, S.M., Hubbard, R.G., Petersen, B.C., 1988. Financing constraints and corporate investment. Brookings Papers on Economic Activity, 141–195. Ehrmann, M., Fratzscher, M., 2004. Taking stock: Monetary policy transmission to equity markets, Journal of Money, Credit and Banking, 36, 719–737. Gagnon, J., Raskin, M., Remache, J., Sack, B., 2011. The financial market effects of the Federal Reserve’s large-scale asset purchases. International Journal of Central Banking, 7, 3–43. Hamilton, J.D., Wu, J.C., 2012. The effectiveness of alternative monetary policy tools in a zero lower bound environment. Journal of Money, Credit and Banking, 44 Supplement, 3–46. Hanson, S.G., Stein, J.C., 2015. Monetary policy and long-term real rates. Journal of Financial Economics, 115, 429–448. Kang, B.K., Kim, T.S., 2006. Option-implied risk preferences: An extension to wider classes of utility functions. Journal of Financial Markets, 9, 180–198.

28

Kiley, M.T., 2014. The response of equity prices to movements in long-term interest rates associated with monetary policy statements: Before and after the zero lower bound. Journal of Money, Credit and Banking, 46, 1057–1071. Li, Y., 2001. Expected returns and habit persistence. Review of Financial Studies, 14, 861–899. Kontonikas, A., MacDonald, R., Aman, S., 2013. State dependence and the financial crises. Journal of Banking and Finance, 37, 4025–4037. Kuttner, K.N., 2001. Monetary policy surprises and interest rates: Evidence from Fed funds futures market. Journal of Monetary Economics, 47, 523–544. Lucca, D.O., Moench, E., 2015. “The pre-FOMC announcement drift. Journal of Finance, 70, 329–371. Rosenberg, J.V., Engle, R.F., 2002. Empirical pricing kernels. Journal of Financial Economics, 64, 341– 372. Ross, S., 2015. The recovery theorem. Journal of Finance, 70, 615–648. Savor, P., Wilson, M., 2013. How much do investors care about macroeconomic risk? Evidence from scheduled economic announcements. Journal of Financial and Quantitative Analysis, 48, 343–375. Tobin, J., 1969. A general equilibrium approach to monetary theory. Journal of Money, Credit, and Banking, 1, 15–29. Stoll, H.R., 1969. The relation between put and call option prices. Journal of Finance, 25, 801–824. Zellner, A, 1962. An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. Journal of the American Statistical Association, 57, 348–368.

29

Appendix A: Implementation issues of OIR This appendix presents details behind implementing the empirical framework described in Section 2. In theory, equation (9) can be used to derive expected returns for all horizons, T. In practice, however, option prices are observable for a limited maturity (usually up to two years) and a limited set of exercise prices, K. Therefore, the implementation of the OIR method requires assumptions on how these limitations of the maturity/exercise price ( T  K ) space can be resolved. Limited set of exercise prices We split the range of exercise prices into two categories. The first category comprises all exercise prices between the minimum and maximum of observable exercise prices conditional upon each maturity. Between the minimum and maximum, we calculate a spline function of the Black-Scholes implied volatilities of (observable) option prices. Dumas et al. (1998) showed that ad hoc smoothed Black-Scholes (1973) implied volatility curves across exercise prices are an appropriate approach to describe the empirically observed implied volatilities. Then, we discretized this range into k = 10,000 steps of length, d (the results are rather insensitive to a finer grid), and employed the spline values for all grid points. Discretization is necessary as the OIR in equation (9) can only be solved numerically. The second category comprises all exercise prices below the minimum or above the maximum. We set the implied volatility of options with an exercise price below the minimum to the implied volatility at the minimum exercise price. For options with a higher exercise price than the maximum, we set the implied volatility to the implied volatility at the maximum. We also discretized the T  K space below the minimum, K, and above the maximum, K, with the same length, d, as described before. This approach follows the literature on how the implied volatility surface of option prices is modeled (e.g., Rosenberg and Engle, 2002). Option maturities We use option maturities up to two years for which data are available. Specifically, we considered option prices for maturities with lengths 1, 3, 6, 9, 12, 18, and 24 months. For these maturities, the OIR and the risk premium can be explicitly calculated, and therefore the news in the risk premium in each future period can be easily approximated by:

30













Et 1 rpi , j  Et 1 rpi , j  Et rpi 1, j 1 ,





where Et rpi , j is the (forward) risk premium from time t  i to time t  j . Please note that in our empirical implementation, Et 1 refers to daily changes in expectations. As our sample contains options with maturities 1, 3, 6, 9, 12, 18, and 24 months, the elements in

 i, j 



include M =



{(0,1),(1,3),(3,6),(6,9),(9,12),(12,18),(18,24 months)}. That is, for example, Et 1 rp3,6 reflects the change in expectations between day t and day t+1 in the forward-risk premium from t+1+3 months to t+1+6 months. The news term for a time horizon greater than two years will be approximated with a decaying approach. That is, we first estimate how changes in forward-risk premiums from time t  j to time t  k (e.g., 18 to 24 months) are related to changes in the forward-risk premium from time t  i to time t  j (e.g., 12 to 18 months):









Et rp j ,k   ijk  Et rpi , j   t .

(A.1)

Therefore, we chose only those forward periods of equal length (e.g., six months). Table A.1 summarizes the various combinations and corresponding estimates of the decay parameter,  ijk . Viewing the table depicts how on average, we observed a decay parameter of approximately 0.75. That is, the forwardrisk premium further in the future changes less than the spot- or forward-risk premium in the near future. TABLE A.1 Regression estimates of Equation (A.1) i

j

12 6 0

18 12 6

6 3 0 average

9 6 3

k

bijk

Length of period j – i = k – j = 6 months 24 0.812 18 0.713 12 0.626 Length of period j – i = k – j = 3 months 12 0.826 9 0.760 6 0.621 0.747

bijk (5%)

bijk (95%)

0.806 0.706 0.822

0.819 0.720 0.830

0.822 0.757 0.617

0.830 0.763 0.624

In our base case, we used a parameter,  ijk , of 0.75 (close to the average of all combinations) for period, j – i = k – j = 6 months, and k  30 months. That is, we modeled changes in future-risk premiums for

31









which we had no option price data as Et rp j ,k  0.75  Et rpi , j . However, changing the parameter to  ijk = 0.9 and  ijk = 0.5 yields similar conclusions for the MP-SR as shown in Table A.2. TABLE A.2 Regression estimates of returns. unexpected returns and their components based on monetary policy news on announcement days of FOMC meetings

Rt 1  a  b  NMPt 1   t 1 , specifications (1)

URt 1  aUR  bUR  NMPt 1   t 1 , specifications (2) N t  A  Dt  A rec  B  NMPt  Dt  B rec  NMPt  Εt , specifications (3a-c) a b a rec Panel A: decay factor 0.75 OLS regression (1) R (2)

UR

SUR regression (3a) NCF (3b)

–NRF

(3c)

–NRP

Panel A: decay factor 0.9 OLS regression (1) R (2)

UR

SUR regression (3a) NCF (3b)

–NRF

(3c)

–NRP

Panel A: decay factor 0.5 OLS regression (1) R (2)

UR

SUR regression (3a) NCF

0.246 ** 0.016 0.214 ** 0.036 0.030 0.729 0.033 0.654 0.151 0.117

0.246 ** 0.016 0.214 ** 0.036 –0.024

0.816 0.033 0.654 0.205 * 0.069

0.246 ** 0.016 0.214 ** 0.036

–9.048 ***

b rec

adj R2

1.047 *** 0.001 1.002 *** 0.001

10.717 *** 0.000 10.676 *** 0.000

0.123

0.313 0.237 –0.156 0.491 0.846 *** 0.005

10.456 *** 0.000 –4.070 ** 0.042 4.289 * 0.099

0.086

–9.048 *** 0.000 –9.007 *** 0.000

1.047 *** 0.001 1.002 *** 0.001

10.717 *** 0.000 10.676 *** 0.000

0.123

–12.671 ***

0.118 0.707 –0.156 0.491 1.040 *** 0.003

11.940 *** 0.000 –4.070 ** 0.042 2.806 0.354

0.089

1.047 *** 0.001 1.002 *** 0.001

10.717 *** 0.000 10.676 *** 0.000

0.123

8.862 *** 0.000 –4.070 ** 0.042 5.884 ** 0.012

0.076

0.000 –9.007 *** 0.000 –10.719 ***

0.000 2.556 0.132 –0.843 0.702

0.000 2.556 0.132 1.108 0.667

–9.048 ***

0.000 –9.007 *** 0.000

0.088 –8.623 *** 0.255 0.000 (3b) –NRF 0.033 2.556 0.654 0.132 (3c) –NRP 0.094 –2.940 0.280 0.139 ***,**,* denotes significance at the 1%, 5%, and 10% level

0.522 ** 0.028 –0.156 0.491 0.637 ** 0.017

0.119

0.119

0.119

32

Appendix B: Consideration of time-varying risk aversion (habit utility) in the OIR approach * Let f t ( ST ) be the real PDF of a stock price in T with information at t. f t ( ST ) is the corresponding

risk-neutral PDF. U T (CT ) denotes the preferences over consumption. Kang and Kim (2006) show that the risk-neutral PDF can be transformed into a real PDF as follows:

ft ( ST ) 



ft * ( ST ) U '( ST ) ft * ( x) U '( x) dx

.

(B.1)

In the case of habit utility preferences, i.e. 1 C X  U (C , X ) 

1 

(B.2)

.

where  is the coefficient of risk aversion, the definition of the consumption surplus ratio,

CSRt   Ct  X t  Ct , can be utilized to rewrite the habit utility in (B.2) as 1 C  CSR   U (C , CSR) 

1 

.

(B.3)

Using equation (B.2) and replacing the marginal utility with the derivation of (B.3) yields:  ST  CSRT   ft * ( ST )  ft ( ST )  .  *   dx x f CSR x ) (   t t 

(B.4)

From Equation (B.4), the expected stock price at different points in time can be easily obtained. Similar to Equation (9), expected dividends between t and t+T have to be considered. It should be noted that the time-varying relative risk aversion coefficient of a habit investor is  CSRt . To be consistent with the risk aversion assumption in the base case, we selected  in such a way that the median risk aversion is two, i.e., median( / CSRt )  2 . 

33

Highlights  Stock returns react differently to interest rate news in recession and boom periods. 

In recessions, the risk premium channel explains largely the stock return.



Then, the stock market rises by 1% independently from the interest rate news.



In boom periods, the cash-flow channel explains mainly the stock return.



Then, interest rate news of -0.25% leads to 2.50% higher cash-flow expectations.

34