Economics and Investment Markets
READING 39
ECONOMICS AND INVESTMENT MARKETS
EXAM FOCUS
This topic review links the real rate of return to investors' inter-temporal rate of substitution. It further uses utility theory to derive the risk premium from the consumption-hedging properties of assets. Be able to identify appropriate risk premiums for different asset classes.
MODULE 39.1: VALUATION AND INTEREST RATES
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LOS 39.a: Explain the notion that to affect market values, economic factors must affect one or more of the following: 1) default-free interest rates across maturities, 2) the timing and/or magnitude of expected cash flows, and 3) risk premiums.
The value of any asset can be computed as the present value of its expected future cash flows discounted at an appropriate risk-adjusted discount rate. The more uncertain the cash flows, the higher the discount rate.
Components of the discount rate are:
- The real risk-free rate (R).
- Expected inflation (π).
- A risk premium reflecting uncertainty about the cash flow (RP).
The value of an asset will change if either the cash flow forecasts change or any of the components of the discount rate changes. Risk premiums not only vary across assets (and asset classes), but also vary with changes in investors' perception of risk. We examine the decomposition of risk premiums for several asset classes in the remainder of this topic review.
LOS 39.b: Explain the role of expectations and changes in expectations in market valuation.
The value of an asset depends on (1) its expected future cash flows and (2) the discount rate used to value those cash flows. As market participants receive new information, the timing and amounts of expected future cash flows are revised and valuations change as a result. The impact of new information will depend on its effect on current expectations so that an earnings report of 53% growth in earnings may have a positive or negative effect on the firm's value, depending on whether expectations were for slower or more rapid growth.
LOS 39.c: Explain the relationship between the long-term growth rate of the economy, the volatility of the growth rate, and the average level of real short-term interest rates.
Even in a world of no inflation, a default-free bond must compensate an investor for forgoing current consumption. The investor evaluates the disutility of forgoing current consumption relative to the utility of obtaining future consumption. The real risk-free rate of interest derives from the inter-temporal rate of substitution, which represents an investor's trade-off between real consumption now and real consumption in the future. Based on utility theory, we can represent this trade-off as follows.
For a given quantity of consumption, investors always prefer current consumption over future consumption (u0 > u1) and the stochastic discount factor for period 1 is typically less than one (m1 < 1) as a result.
The current price (P0) of a zero-coupon, inflation-indexed, risk-free bond that will pay $1 at time 1 can be expressed as:
P0 = E(m1)
In which case, the real risk-free gross return is:
1 + R = 1 / P0
and therefore the real risk-free rate of return is:
R = 1 / P0 - 1
PROFESSOR'S NOTE
We have been considering an inflation-indexed bond in this example because we do not want to consider the effects of inflation in our analysis yet.
Some key points to keep in mind:
- The higher the utility investors attach to current consumption relative to future consumption, the higher the real rate.
- Diminishing marginal utility of wealth means that an investor's marginal utility of consumption declines as wealth increases. This suggests that marginal utility of consumption is higher during periods of scarcity, such as during economic contractions.
- If investors expect higher incomes in the future, their expected marginal utility of future consumption is decreased relative to current consumption. When investor expectations about the economy change to better economic times ahead, the expectation of higher incomes in the future will lead to an increase in current consumption and a reduction in savings. Investors will derive greater utility from current consumption relative to future consumption and would, therefore, save less. Conversely, investors expecting worse times ahead would prefer to increase future consumption by reducing current consumption and saving more.
- Investors increase their savings rate when expected returns are high or when uncertainty about their future income increases.
Risky Cash Flows and Risk Premiums
The risk aversion of investors can be explained by the covariance of an investor's inter-temporal marginal rate of substitution and expected returns on savings. Our discussion so far was limited to risk-free investments. However, if the underlying cash flows are uncertain, investors demand a risk premium for bearing the risk that comes with such uncertainty. The investor's expected marginal utility of a payoff is inversely related to the level of uncertainty of the payoff. Investors experience a larger loss of utility for a loss in wealth as compared to a gain in utility for an equivalent gain in wealth. This property is called risk aversion.
An investor's absolute risk aversion declines with their wealth; wealthier investors are less risk-averse and more willing to take risk relative to their poorer counterparts. However, the marginal utility of holding risky assets declines as an investor holds more risky assets in her portfolio. When markets are in equilibrium, wealthy and poorer investors would have the same willingness to hold risky assets.
Consider a risk-free, inflation-indexed, zero-coupon bond that an investor will sell prior to maturity. The uncertainty about the sale price gives rise to a risk premium. The price of the bond will be lower than the expected sale price discounted at the real risk-free rate. We can model this risk premium by using the stochastic discount factor representation:
The valuation equation for any asset with random payoff P1 is:
P0 = E[m1 × P1]
We can decompose the right-hand side using the properties of expectation:
P0 = E(m1) × E(P1) + Cov(m1, P1)
Recall that for a risk-free bond the real risk-free gross return equals 1 / E(m1). Using that relation, the expected sale price discounted at the real risk-free rate is:
E(P1) / (1 + R) = E(P1) × E(m1)
The difference between the expected-sale-price discounted at the real risk-free rate and the actual current price equals the covariance term:
E(P1) / (1 + R) - P0 = -Cov(m1, P1)
Therefore the risk premium arising from the uncertain sale price is directly related to the covariance between the investor's stochastic discount factor and the asset's payoff. For risk-averse investors, when the covariance is negative (typical for many risky assets), the current price P0 is lower than the expected-sale-price discounted at the risk-free rate; accordingly expected returns are higher due to the positive risk premium.
In the context of a risky asset (for example, stocks), for risk-averse investors the covariance is likely to be negative. When the expected future price of the asset is high, the marginal utility of future consumption relative to current consumption is low because during good economic times both labour incomes and most risky asset values are high. With higher future labour incomes, the marginal utility of future consumption is lower. The resulting negative covariance between the marginal utility of consumption (captured by m1) and asset prices reduces the value of the asset for a given expected sale price, P1. All else constant, the lower current price (P0) increases expected return. This higher expected return is due to a positive risk premium.
For a single-period, truly risk-free bond, the covariance is zero because there is no uncertainty about the terminal value; there is no risk premium in that case.
GDP Growth Rates
If GDP growth is forecast to be high, the utility of consumption in the future (when incomes will be high) will be low and the inter-temporal rate of substitution will fall; investors will save less, increasing real interest rates. Therefore, real interest rates will be positively correlated with real GDP growth rates. This is consistent with the existence of high real rates in rapidly growing developing economies such as India and China. Interest rates are also positively correlated with the expected volatility in GDP growth due to higher risk premiums.
LOS 39.d: Explain how the phase of the business cycle affects policy and short-term interest rates, the slope of the term structure of interest rates, and the relative performance of bonds of differing maturities.
So far we have not considered the implications of inflation in our analysis of the correlation between interest rates and GDP growth. Nominal risk-free interest rates include a premium for expected inflation (π). However, actual inflation is uncertain. This additional uncertainty gives rise to an additional risk premium for the uncertainty about actual inflation (θ). This risk premium is generally higher for longer-maturity bonds.
For short-term risk-free securities (for example, T-bills), the uncertainty about inflation over the short interval is often negligible and, therefore, the nominal interest rate (r) would be comprised of the real risk-free rate (R) and expected inflation (π):
r(short-term) = R + π
For longer-term bonds, we add the risk premium for uncertainty about inflation, θ:
r(long-term) = R + π + θ
Taylor Rule
Central banks are usually charged with setting policy rates so as to (1) maintain price stability and (2) achieve the maximum sustainable level of employment. The Taylor rule links the central bank's policy rate to economic conditions (output gap and inflation). A commonly used form of the rule is:
i = r* + π + 0.5(π - π*) + 0.5(y - y*)
where i is the nominal policy rate, r* the long-run real equilibrium rate, π current inflation, π* the inflation target, and y - y* the output gap. Central banks can moderate the business cycle by making appropriate changes to the policy rate or can magnify the cycle by not responding appropriately to changing economic conditions (for example, committing policy errors such as keeping rates too low).
Business Cycle and Slope of the Yield Curve
When the economy is in recession, policy rates tend to be low. As the economy comes out of recession, investors' improving expectations about future GDP growth and increasing inflation lead to higher longer-term rates. This results in a positively sloped yield curve. Conversely, expectations of a decline in GDP growth result in a negatively sloped (inverted) yield curve. For this reason, an inverted yield curve is often considered a predictor of future recessions. Later stages of an economic expansion often are characterised by high inflation and high short-term interest rates, while longer-term rates may be lower, reflecting investors' expectations of decreasing inflation and GDP growth.
A term spread is the difference between the yield on a longer-term bond and the yield on a short-term bond. Evidence suggests that a normal term spread is positive so the yield curve is upward sloping. Recall that the risk premium for uncertainty in inflation (θ) is higher for longer-maturity bonds. Positive term spreads can be attributed in part to an increasing θ for longer periods.
LOS 39.e: Describe the factors that affect yield spreads between non-inflation-adjusted and inflation-indexed bonds.
The difference between the yield of a non-inflation-indexed risk-free bond and the yield of an inflation-indexed risk-free bond of the same maturity is the break-even inflation rate (BEI).
BEI = yield on non-inflation-indexed bond - yield on inflation-indexed bond
Recall that for longer maturity bonds, the nominal rate is composed of the real rate, expected inflation, and a risk premium for inflation uncertainty. Therefore, BEI is composed of two elements: expected inflation (π) and a risk premium for uncertainty about actual inflation (θ).
BEI = π + θ
LOS 39.f: Explain how the phase of the business cycle affects credit spreads and the performance of credit-sensitive fixed-income instruments.
The required rate of return for bonds with credit risk includes an additional risk premium. This credit risk premium (credit spread) is the difference in yield between a credit-risky bond and a default-free bond of the same maturity.
Required rate of return for credit-risky bonds = R + π + θ + γ
where:
- γ = additional risk premium for credit risk = credit spread
Credit spreads tend to rise during times of economic downturns and fall during expansions. Research has shown that defaults increase and recovery rates decrease during periods of economic weakness. Both effects result in greater credit losses during economic downturns.
When credit spreads narrow, credit-risky bonds will typically outperform default-free bonds. Overall, lower-rated bonds tend to benefit more than higher-rated bonds from a narrowing of credit spreads (their yields fall more). Conversely, when credit spreads widen, higher-rated bonds will outperform lower-rated bonds on a relative basis (because their yields will rise less).
MODULE QUIZ 39.1
1. Carrier, Inc.'s stock price fell last week, which was contrary to the movement in the industry index. Which of the following is most likely a valid reason for that to occur?
A. An increase in the real risk-free rate.
B. Inflation is expected to be higher.
C. Investors are demanding a higher risk premium on Carrier.
2. Sonic, Inc., reported 12% earnings growth year-over-year, but its stock price fell. Which of the following is the most likely explanation?
A. Sonic's stock price included an event risk premium prior to the earnings announcement.
B. The market's expectation was for Sonic to report an earnings growth of more than 12%.
C. Market sentiment is often subjective and biased.
3. Which of the following statements is most accurate? Higher expected GDP growth would:
A. lower the utility of future consumption and reduce the inter-temporal rate of substitution.
B. increase the utility of future consumption and reduce the inter-temporal rate of substitution.
C. lower the utility of future consumption and increase the inter-temporal rate of substitution.
4. Break-even inflation rate is comprised of the:
A. real rate and unexpected inflation.
B. expected inflation and risk premium for inflation uncertainty.
C. inter-temporal rate of substitution and expected inflation.
5. An economy just getting out of recession would most likely have:
A. high short-term rates and an inverted yield curve.
B. low short-term rates and an inverted yield curve.
C. low short-term rates and an upward sloping yield curve.
6. Zeon Corp's 10-year bonds are currently yielding 7.50%. The real rate is 3% and expected inflation is 2%. Which of the following is most accurate? Credit spread on Zeon bonds is:
A. equal to 2.50%.
B. less than 2.50%.
C. greater than 2.50%.
MODULE 39.2: THE BUSINESS CYCLE
LOS 39.g: Explain how the characteristics of the markets for a company's products affect the company's credit quality.
Video covering this content is available online.
Analysis of credit spreads by industrial sectors reveals that spreads differ among sectors and over time. Differences in credit spreads are primarily due to differences in industry products and services and the financial leverage of the firms in the industry. Spreads for issuers in the consumer cyclical sector increase significantly during economic downturns compared to spreads for issuers in the consumer non-cyclical sector.
LOS 39.h: Explain the relationship between the consumption-hedging properties of equity and the equity risk premium.
The discount rate used to value equity securities includes an additional risk premium, the equity risk premium. This risk premium is in addition to the risk premium on credit-risky bonds because equity is more risky than debt.
Discount rate for equity = R + π + θ + γ + κ
where:
- κ = additional risk premium relative to risky debt for an investment in equities
- λ = equity risk premium = γ + κ
Assets that provide a higher payoff during economic downturns are more highly valued because of the consumption-hedging property of the asset. This property reduces the risk premium on an asset. Equity prices are generally cyclical, with higher values during economic expansions when the marginal utility of consumption is lower. Equity investments, therefore, are not the most effective hedge against bad consumption outcomes. Because of this poor consumption-hedging ability, the equity risk premium is positive.
LOS 39.i: Explain how the phase of the business cycle affects short-term and long-term earnings growth expectations.
Corporate earnings may be related to the business cycle. Cyclical industries (for example, durable goods manufacturers and consumer discretionary) tend to be relatively more sensitive to the phase of the business cycle. Companies in these industries have revenues and earnings that rise and fall with the rate of economic growth. Defensive or non-cyclical industries (for example, consumer non-discretionary) tend to be relatively immune to fluctuations in economic activity; their earnings tend to be relatively stable throughout the business cycle.
LOS 39.j: Describe cyclical effects on valuation multiples.
Price multiples such as P/E and P/B are often used in determining the relative values of companies, sectors, or the overall market from a historical perspective. However, it is inappropriate to judge the multiple in a historical context only. If the P/E ratio for an index (for example, the S&P 500) is above historical standards, it could be that the index is overvalued, but it also could be that the index level is justified by current conditions.
Price multiples are positively correlated with expected earnings growth rates and negatively correlated with required returns. Therefore, price multiples rise with increases in expected future earnings growth and with a decrease in any of the components of the required rate of return (the real rate, expected inflation, the risk premium for inflation uncertainty, or the equity risk premium). As a result, the equity risk premium declines during economic expansions and rises during recessions.
Shiller's CAPE (real cyclically adjusted P/E) ratio reduces the volatility of unadjusted P/E ratios by using real (inflation-adjusted) prices in the numerator and a 10-year moving average of real earnings in the denominator.
LOS 39.k: Describe the economic factors affecting investment in commercial real estate.
Commercial real estate investments have:
- Bond-like characteristics. The steady rental income stream is similar to cash flows from a portfolio of bonds. Furthermore, just as the credit quality of issuers affects the value of a bond portfolio, the credit quality of tenants affects the value of commercial real estate.
- Equity-like characteristics. The value of commercial real estate is influenced by many factors, including the state of the economy, the demand for rental properties, and property location. Uncertainty about the value of the property at the end of the lease term gives commercial properties an equity-like character.
- Illiquidity. Real estate as an asset class is characterised by illiquidity; it could take years to exit a real estate investment at its fair value.
Valuation
When estimating the value of real estate investment, the discount rate includes an additional risk premium for the lack of liquidity:
Discount rate for commercial real estate = R + π + θ + γ + κ + φ
where:
- κ = risk premium for uncertainty about terminal value of property (similar to the equity risk premium)
- φ = risk premium for illiquidity
While rental income from commercial properties seems to be more or less steady across business cycles, commercial property values tend to be very cyclical. Because of this, the correlation of commercial property values with those of other asset classes (for example, equities) tends to be positive. Similar to equities, real estate provides a poor hedge against bad consumption outcomes. Therefore, the risk premium required by investors for investment in commercial properties will be relatively high and often close to the risk premium required for equity investments.
MODULE QUIZ 39.2
1. Compared to the credit spreads of issuers classified as consumer non-cyclical, during economic downturns credit spreads on issuers classified as consumer cyclical are most likely to widen:
A. more.
B. less.
C. approximately the same amount.
2. Earnings of companies in the consumer staples industry are most likely to:
A. fluctuate with the business cycle.
B. remain stable over the business cycle.
C. fluctuate more than companies in consumer discretionary industries.
3. Which of the following statements is most accurate? Equity as an asset class provides:
A. good consumption hedging properties and, therefore, commands a positive risk premium.
B. poor consumption hedging properties and, therefore, commands a positive risk premium.
C. good consumption hedging properties and, therefore, commands a negative risk premium.
4. Analysis of price multiples is most likely to indicate that the equity risk premium:
A. declines during economic downturns.
B. is stable over the business cycle.
C. declines over economic expansions.
5. Relative to other asset classes, investors in commercial real estate are least likely to require a risk premium for:
A. uncertainty in inflation.
B. illiquidity.
C. uncertainty in terminal value.
KEY CONCEPTS
LOS 39.a
The value of any asset can be computed as the present value of its expected future cash flows discounted at an appropriate risk-adjusted discount rate. Risky cash flows require the discount rate to be higher due to inclusion of a risk premium.
LOS 39.b
Market prices reflect current expectations. Only changes in expectations cause a change in market price.
LOS 39.c
Interest rates are positively related to GDP growth rate and to the expected volatility in GDP growth due to a higher risk premium.
LOS 39.d
When the economy is in recession, short-term policy rates tend to be low. Investor expectations about higher future GDP growth and inflation as the economy comes out of recession lead to higher longer-term rates. This leads to a positive slope of the yield curve. Conversely, an inversely sloping yield curve is often considered a predictor of future recessions.
LOS 39.e
Break-even inflation rate (BEI)
= yield on non-inflation-indexed bonds - yield on inflation-indexed bonds
BEI is comprised of two elements: expected inflation (π) and risk premium for uncertainty in inflation (θ).
LOS 39.f
Credit spreads tend to rise during times of economic downturns and shrink during expansions. When spreads narrow, lower-rated bonds tend to outperform higher-rated bonds.
LOS 39.g
Spreads for issuers in the consumer cyclical sector widen considerably during economic downturns compared to spreads for issuers in the consumer non-cyclical sector.
LOS 39.h
Equities are generally cyclical; they have higher values during good times and have poor consumption-hedging properties. Therefore, the risk premium on equities should be positive.
LOS 39.i
Cyclical industries (for example, durable goods manufacturers and consumer discretionary) tend to be extremely sensitive to the business cycle; their earnings rise during economic expansions and fall during contractions. Non-cyclical or defensive industries tend to have relatively stable earnings.
LOS 39.j
Price multiples tend to follow the business cycle: multiples rise during economic expansions (as analysts revise growth estimates upward) and fall during contractions (as growth estimates are revised downward).
LOS 39.k
Commercial real estate has equity-like and bond-like characteristics. The valuation depends on the rental income stream, the quality of tenants, and the terminal value at the end of the lease term. The discount rate for commercial real estate includes a risk premium for uncertainty in terminal value and also for illiquidity.
ANSWER KEY FOR MODULE QUIZZES
Module Quiz 39.1
1. C If the real risk-free rate had increased or expected inflation had been higher, the discount rate would have been higher and would have lowered both Carrier's stock price and the industry index. Given the divergence between Carrier's stock price and the industry index, a higher risk premium for Carrier's stock is the only valid reason from the choices provided. (LOS 39.a)
2. B Market prices embed current expectations. If the market reaction to earnings growth of 12% was negative, it would mean that the market prices were based on a higher earnings growth rate expectation. (LOS 39.b)
3. A A higher GDP growth rate would mean higher incomes in the future. Due to the principle of diminishing marginal utility, the utility of future consumption would therefore be lower. Lower future utility relative to the utility of current consumption lowers the inter-temporal rate of substitution. (LOS 39.c)
4. B BEI = expected inflation + risk premium for uncertainty in inflation. (LOS 39.e)
5. C An economy just getting out of recession is more likely to have low short-term rates, as the central bank policy rate would be low. Higher future GDP growth prospects would mean higher real rates and higher expected inflation over the longer term, so long-term rates would be high, leading to an upward sloping yield curve. (LOS 39.d)
6. B Yield on risky corporate debt = real risk-free rate + expected inflation + risk premium for inflation uncertainty + credit spread. 2.50% = risk premium for inflation uncertainty + credit spread. Given that the bond is long term, the risk premium for inflation uncertainty must be positive and the credit spread must be less than 2.50%. (LOS 39.f)
Module Quiz 39.2
1. A Credit spreads on consumer cyclical issuers widen during economic downturns and narrow during economic expansions. (LOS 39.g)
2. B Earnings of consumer staples companies tend to be relatively stable over the entire business cycle. (LOS 39.i)
3. B Stocks in general tend to perform well during economic expansions and, therefore, pay off during good economic times. The property of performing poorly during bad economic times implies that equities are a poor consumption hedge. Because they are a poor consumption hedge, investors demand a positive risk premium for investing in equities. (LOS 39.h)
4. C Price multiples tend to expand during economic expansions, suggesting that the equity risk premium declines during expansions. This is because investors become less risk averse during economic expansions and demand a lower premium for taking risk. (LOS 39.j)
5. A Two risk premiums that are unique to real estate as an asset class are the risk premium for illiquidity and the risk premium for uncertainty in terminal value (similar to the equity risk premium). (LOS 39.k)
