Portfolio management Part 1

Question 1

What are the components of the discount rates?

Answer 1

1. The real risk-free rate
2. Expected inflation
3. A risk premium reflecting uncertainty about the cash flow (RP)

Question 2

How is the value of an asset computed?

Answer 2

PV of expected cashflow, discounted at appropriate risk- adjusted discount rate.

Most uncertain the cashflow -< the higher discount rate.

Question 3

What factors can cause the value of an asset to change?

Answer 3

The value of an asset can change if:

• Cash flow forecasts change
• Any component of the discount rate changes (e.g., risk-free rate, risk premium)
  Risk premiums vary across assets and asset classes, and can also change with investor perceptions of risk.

Question 4

What are the 2 decompose factor that the value of an asset depends on?

Answer 4

1) Expected future cashflow
2) discount rate

Question 5

What is the role of expectations and changes in expectations in market valuation? How does new information change the following?

Answer 5

New information leads market participants to revise expectations, affecting valuations. The impact depends on how the news compares to prior expectations—for example, 53% earnings growth may increase or decrease value depending on whether it exceeds or falls short of what was expected.

Question 6

What is the inter-temporal rate of substitution?

Answer 6

Investors trade-off between real consumption now and real consumption in the future

Question 7

The tradeoff of inter-temporal rate of substitution.

Answer 7

Inter-temporal rate of substitution = marginal utility of consuming 1 unit in the future at time t / marginal utility of current consumption of 1 unit

Question 8

What does the risk-free rate represent

Answer 8

With no inflation, a default free bond has to compensate an investor for forgoing their current consumption.

Question 9

Take an inflation-indexed bond, calculate the risk-free rate

Answer 9

Question 10

How do consumption preferences, expected income, and uncertainty affect the real interest rate?

Answer 10

Higher preference for current consumption → higher real interest rate

Diminishing marginal utility of wealth → consumption has more value during economic contractions

Expectations of higher future income → lower marginal utility of future consumption → less saving, higher real rates

Expectations of lower future income or uncertainty → more saving, driving real rates down

Higher expected returns or higher income uncertainty → increased saving

Question 11

What drives real risk free rates?

Answer 11

• Higher preference for current consumption -> higher real interest rates
• Diminishing marginal utility of wealth; wealthier each additional dollar adds less satisfaction

Tough times -> consumption has more value → people save more → lower real interest rates. (expected future income is low)

Good times: marginal utility of future consumption is low, so people save less → higher real rates. (expected future income is high)

Question 12

What does risk aversion mean?

Answer 12

Investors hate losses more than they enjoy equivalent gain.

-> They demand a risk premium to hold assets with uncertain (risky) future cash flows.

Question 13

What is risk aversion in investing?

Answer 13

Risk aversion means investors dislike losses more than they enjoy equivalent gains. → A $100 loss feels worse than the joy from a $100 gain. → So, investors demand extra return (risk premium) to hold risky assets.

Question 14

Why do investors demand a risk premium?

Answer 14

Because risky assets have uncertain future cash flows, investors face potential losses. To be compensated for this uncertainty, they demand a risk premium—an expected return above the risk-free rate.

Question 15

What happens to marginal utility of wealth as wealth increases?

Answer 15

It decreases (diminishing marginal utility). → Each extra dollar is less valuable when you’re already wealthy. → During bad times (low wealth), each dollar means more, increasing marginal utility.

Question 16

How is risk premium related to covariance with utility?

Answer 16

Risk premium arises from the covariance between asset payoffs and marginal utility of consumption. If an asset pays off in good times → utility is low → value is low → requires higher return. This negative covariance → positive risk premium.

Question 17

What is the formula involving risk premium and utility?

Answer 17

P₀ = E(P₁)/(1 + R) + cov(P₁, m₁) → P₀: current asset price; E(P₁): expected future price; R: real risk-free rate; cov(P₁, m₁): covariance with marginal utility → Negative covariance = lower price = higher expected return = risk premium.

Question 18

Why don’t risk-free bonds have a risk premium?

Answer 18

Because their future payoff is certain → no uncertainty → covariance = 0. So, they are priced using only the real risk-free rate, with no risk premium.

Question 19

Risk aversion

Answer 19

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.

Question 20

For a single period risk free bond, what is its covariance

Answer 20

For a single-period risk-free bond, the covariance is zero as there is no uncertainty about the terminal value; there is no risk premium.

Question 21

What is the correlation of interest rates and GDP growth rates

Answer 21

Positively correlated.

If GDP growth is forecasted 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.

Question 22

What is the correlation between interest rates, and expected volatility in GDP growth

Answer 22

Positively

Because higher risk premium

Question 23

What is nominal risk free interest rates

Answer 23

Adds premium for expected inflation

• Actual inflation is uncertain
• Adds a premium, for uncertainty of expected inflation
• Higher for longer maturity bonds

Question 24

For short term, what do we do with the uncertainty of inflation (like t-bills).

Answer 24

Uncertainty is negligible

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

Question 25

What is the purpose of the Taylor Rule?

Answer 25

The Taylor Rule helps central banks set policy rates to maintain price stability and achieve maximum sustainable employment by linking rates to inflation and output gaps.

Question 26

What is the formula for the Taylor Rule?

Answer 26

r = Rn + π + 0.5(π – π*) + 0.5(y – y*)

Question 27

What do the variables in the Taylor Rule represent?

Answer 27

r: implied policy rate, Rn: neutral real rate, π: current inflation, π*: target inflation, y: log of current output, y*: log of target output.

Question 28

How can central banks influence the business cycle using the policy rate?

Answer 28

By raising or lowering policy rates in response to economic conditions, central banks can either stabilize or unintentionally amplify the business cycle.

Question 29

What does the slope of the yield curve indicate about the business cycle?

Answer 29

A positively sloped yield curve suggests future economic growth and inflation, while an inverted yield curve often signals an upcoming recession.

Question 30

What is a term spread and what does it typically look like?

Answer 30

Term spread = yield on long-term bond – yield on short-term bond. It’s usually positive, creating an upward-sloping yield curve due to higher inflation risk (θ) over time.

Question 31

What is the break-even inflation rate (BEI)?

Answer 31

BEI = yield on non-inflation-indexed bond – yield on inflation-indexed bond. It reflects the market's expected inflation and a premium for inflation uncertainty.

Question 32

What are the components of the break-even inflation rate (BEI)?

Answer 32

BEI = π + θ, where π is expected inflation and θ is the risk premium for inflation uncertainty.

Question 33

What is the required rate of return for credit risky bonds?

Answer 33

Required return = R + π + θ + γ, where γ is the credit spread, an additional risk premium for credit risk.

Question 34

How do credit spreads behave across the business cycle?

Answer 34

Credit spreads widen during economic downturns (higher defaults, lower recovery) and narrow during expansions.

Question 35

How does the performance of credit-sensitive bonds change with credit spreads?

Answer 35

When credit spreads narrow, lower-rated bonds outperform. When spreads widen, higher-rated bonds outperform on a relative basis.

Question 36

Break-even inflation rate is comprised of the:

Answer 36

expected inflation and risk premium for inflation uncertainty.

Question 37

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.

Answer 37

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.

Question 38

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 What is it for equity investments?

Answer 38

- They are generally cyclical - Higher values during economic expansions when the marginal utility of consumption is lower - Equity are not effective hedge against bad consumption outcomes

Question 39

How do product market characteristics affect a company's credit quality?

Answer 39

Credit spreads differ by industry due to differences in products/services and leverage. Consumer cyclical sectors see greater spread increases in downturns than consumer non-cyclicals.

Question 40

What is the relationship between equity's consumption hedging and the equity risk premium? (LOS 34.h)

Answer 40

Equities offer poor hedging against bad consumption outcomes, so they require a positive equity risk premium: λ = γ + κ, where κ is the equity-specific premium.

Question 41

What is the discount rate formula for valuing equities? (LOS 34.h)

Answer 41

Discount rate for equity = R + π + θ + γ + κ

Question 42

How does the business cycle affect earnings growth expectations? (LOS 34.i)

Answer 42

Cyclical industries have earnings that rise/fall with the economy (e.g., durable goods manufacturers and consumer discretionary), while defensive industries (e.g., consumer non-discretionary) show stable earnings across the business cycle.

Question 43

What are the cyclical effects on valuation multiples like P/E and P/B?

Answer 43

Multiples rise with higher expected earnings growth and lower required returns. Equity risk premiums fall in expansions and rise in recessions.

Question 44

What does Shiller's CAPE ratio adjust for? (LOS 34.j)

Answer 44

It reduces P/E volatility by using real prices and a 10-year moving average of real earnings.

Question 45

What are the key characteristics of commercial real estate investments? (LOS 34.k)

Answer 45

They have bond-like rental income, equity-like terminal value uncertainty, and are illiquid. Tenant credit quality impacts value.

Question 46

What is the discount rate formula for commercial real estate? (LOS 34.k)

Answer 46

Discount rate = R + π + θ + γ + κ + φ, where φ is the illiquidity premium. κ = risk premium for uncertainty about terminal value of property (similar to the equity risk premium) φ = risk premium for illiquidity

Question 47

Why does commercial real estate have a high risk premium? (LOS 34.k)

Answer 47

Because it's illiquid and has equity-like characteristics, it's poorly correlated with bad consumption outcomes and thus requires a high risk premium.

Question 48

Correlation between price multiples with expected earnings growth rates price multiples correlation with required returns

Answer 48

- Positively - Negatively 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.

Question 49

Bond-like characteristics.

Answer 49

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.

Question 50

Equity-like characteristics.

Answer 50

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.

Question 51

Illiquidity

Answer 51

Real estate as an asset class is characterized by illiquidity; it could take years to exit a real estate investment at its fair value.

Question 52

Correlation with price multiples -> earnings growth -> components of the discount rate

Answer 52

Price multiples are positively related to earnings growth and negatively related to each of the components of the discount rate (i.e., real rate, inflation premium, equity risk premium).