Inv. Analysis (93)

If the real interest rate is 6% and expected inflation is 2%, what is the approximate nominal interest rate?

8% — Nominal ≈ real + expected inflation = 6% + 2% = 8%.

A stock is bought at $25, pays a $1 dividend, and is sold at $29. What is the holding-period return (HPR)?

20% — HPR = (29 − 25 + 1) / 25 = 20%.

What determines the level of real interest rates?

All three: the supply of savings by households, the demand for investment funds by businesses, and government net borrowing or lending.

Ceteris paribus, what does a decrease in the demand for loans do to interest rates?

It drives interest rates down.

The HPR on a stock equals the sum of which two yields?

Capital gains yield plus dividend yield.

What do historical 1926–2021 returns on stocks, Treasury bonds, and T-bills show?

Stocks offered higher average returns than bonds and T-bills.

KMP stock: Boom (prob 0.30) 18%; Normal (0.50) 12%; Recession (0.20) −5%. What is the expected HPR?

10.40% — 0.30(18%) + 0.50(12%) + 0.20(−5%) = 10.4%.

According to the theory of risk-averse investors, what is the risk premium on common stocks?

It must be a positive expected risk premium.

Portfolio return 18%, risk-free rate 5%, standard deviation of excess return 34%. What is the risk premium?

13% — Risk premium = 18% − 5% = 13%.

Duke stock is bought for $90, pays a $3 dividend, and is sold for $92. What is the HPR?

5.56% — HPR = (92 − 90 + 3) / 90 = 5.56%.

Portfolio return 11%, risk-free rate 6%, standard deviation 25%. What is the risk premium?

5% — Risk premium = 11% − 6% = 5%.

The real interest rate is approximately equal to what?

The nominal interest rate minus the inflation rate.

A bond is bought at $980, pays $17 interest, and is sold for $987 after 63 days. What is the HPR?

2.45% — HPR = (987 − 980 + 17) / 980 = 2.45%.

Nominal interest is 8% and inflation is 3.5%. What is the exact real growth in purchasing power?

4.35% — Exact real return = (1.08 / 1.035) − 1 ≈ 4.35%.

A $1,000 savings account earns 6% while inflation is 2%. What is the approximate real return?

4% — 6% − 2% = 4%.

Real interest rate 4%, expected inflation 2%. What is the approximate nominal interest rate?

6% — 4% + 2% = 6%.

A stock is bought for $12, pays a $0.50 dividend, and is sold for $13.25. What is the HPR?

14.58% — HPR = (13.25 − 12 + 0.50) / 12 = 14.58%.

Which risk measure highlights the potential loss from extreme negative returns?

Value at Risk (VaR).

Which measure lets you compare investments with different time horizons?

The effective annual rate (EAR).

How is the APR (annual percentage rate) computed?

Using simple interest: the per-period rate is annualized without compounding.

An investment provides a 2% semiannual return. What is its EAR?

4.04% — EAR = (1.02)^2 − 1 = 4.04%.

An investment provides a 0.78% monthly return. What is its EAR?

9.77% — EAR = (1.0078)^12 − 1 ≈ 9.77%.

Portfolio return 8%, risk-free rate 3%, standard deviation 20%. What is the Sharpe measure?

0.25 — Sharpe = (8% − 3%) / 20% = 0.25.

A portfolio has a Sharpe ratio of 0.83. Benchmarks have Sharpe ratios of 0.81, 0.79, 0.65, and 0.62. Against which benchmarks did the portfolio outperform?

All of them (0.83 is higher than every benchmark).

What is the best general measure of a portfolio's risk-adjusted performance?

The Sharpe measure.

What is true about risk-averse investors?

They require a positive expected risk premium to invest in risky assets.

David is less risk-averse than Elias. What is true?

For the same return, David will tolerate more risk than Elias.

Which factor is LEAST likely to be used in assessing an investor's risk tolerance?

The investor's preferred level of return.

Using U = E(r) − 0.6σ^2, which investment do you choose: (12% return, 20% SD), (10%, 15%), (10%, 10%), or (8%, 10%)?

12% expected return and 20% standard deviation (utility = 9.60%). — U = 0.12 − 0.6(0.20)^2 = 0.096, the highest of the four.

Under mean-variance dominance, which is best: E(r)=0.15/variance 0.20, E(r)=0.10/var 0.20, E(r)=0.10/var 0.25, or E(r)=0.15/var 0.25?

E(r) = 0.15 with variance = 0.20 (highest return at the lowest risk).

Portfolio A has a 15% expected return and 15% SD. Which portfolio might lie on the same indifference curve?

A portfolio with a 10% expected return and 10% SD (lower return paired with lower risk).

Can investors' exact indifference curves be known?

Not with certainty, but estimates help determine suitable portfolios.

What does the presence of risk mean?

More than one outcome is possible.

Other things equal, how does the utility score change with expected return?

Utility increases as expected return increases.

What is the certainty equivalent rate?

The guaranteed risk-free rate that an investor finds equally attractive as the risky portfolio.

Mean-variance criterion: A (10%, 5%), B (21%, 11%), C (18%, 23%), D (24%, 16%) [return, SD]. Which dominance statement is correct?

B dominates C (higher return and lower risk).

What does the capital allocation line (CAL) describe?

The opportunity set of combinations of the risk-free asset and a risky portfolio.

Which statement about the CAL is FALSE?

That the CAL is the efficient frontier of risky assets in the absence of a risk-free asset.

The optimal portfolio on a given CAL maximizes what?

Expected utility.

You invest 40% in a risky portfolio (E = 0.15, variance = 0.04) and 60% in T-bills at 6%. What are the expected return and SD?

Expected return 0.096; SD 0.08. — E = 0.4(0.15) + 0.6(0.06) = 0.096; SD = 0.4(0.20) = 0.08.

You invest 40% in a risky portfolio (E = 0.13, variance = 0.03) and 60% in T-bills at 6%. What are the expected return and SD?

Expected return 0.088; SD 0.069. — E = 0.4(0.13) + 0.6(0.06) = 0.088; SD = 0.4(√0.03) = 0.069.

You invest 70% in a risky portfolio (E = 0.15, variance = 0.04) and 30% in T-bills at 5%. What are the expected return and SD?

Expected return 0.120; SD 0.14. — E = 0.7(0.15) + 0.3(0.05) = 0.12; SD = 0.7(0.20) = 0.14.

The risky portfolio returns 12% and T-bills 5%. To target a 9% return, how do you split between the risky portfolio and T-bills?

57% risky; 43% T-bills. — w = (9% − 5%) / (12% − 5%) = 0.571.

T-bills yield 5%. Risky portfolio P is 60% stock X (14%) and 40% stock Y (10%). To earn 10%, what weights go to T-bills, X, and Y?

T-bills 0.32; X 0.41; Y 0.27. — E(P) = 0.6(14%) + 0.4(10%) = 12.4%. Risky weight = (10% − 5%) / (12.4% − 5%) = 0.6757. X = 0.6757 × 0.6 = 0.41; Y = 0.6757 × 0.4 = 0.27; T-bills = 0.32.

What is a reward-to-volatility ratio useful for?

Understanding how returns increase relative to increases in risk.

What is the first major step in asset allocation?

Assessing risk tolerance.

What may asset allocation involve?

Allocating between a risk-free asset and risky assets, and allocating among different risky assets.

On a mean–standard deviation graph, what line connects the risk-free rate with the optimal risky portfolio P?

The capital allocation line (CAL).

Why are Treasury bills commonly viewed as risk-free assets?

Their short maturities make prices relatively insensitive to interest-rate changes, and inflation uncertainty over their maturity is negligible.

Bo Regard has 80% in portfolio P (expected return 12%) and 20% in T-bills (3.6%). What is the expected return of his complete portfolio?

10.32% — 0.8(12%) + 0.2(3.6%) = 10.32%.

Which statements about the capital market line (CML) are correct? (I) it is a special CAL; (II) it is the passive-strategy opportunity set; (III) the one-month T-bill is the intercept; (IV) a broad stock index is the risky-portfolio proxy.

I, II, III, and IV — all are correct.

How does the standard-deviation reduction of a 100-stock well-diversified portfolio compare to that of a 200-stock portfolio?

Not significantly different.

Market risk is also referred to as what?

Systematic risk or nondiversifiable risk.

Diversifiable risk is also referred to as what?

Unique risk or firm-specific risk.

How is the variance of a portfolio of risky securities calculated?

As a weighted sum of the securities' variances and covariances.

What does the standard deviation of a portfolio of risky securities equal?

The square root of the weighted sum of the securities' variances and covariances.

What does the expected return of a portfolio of risky securities equal?

A weighted average of the securities' expected returns.

Other things equal, when is diversification most effective?

When the securities' returns are negatively correlated.

Which part of the minimum-variance frontier is the efficient frontier of risky assets?

The upper branch, lying above the global minimum-variance portfolio.

What is the CAL provided by a risk-free security combined with N risky securities?

The line from the risk-free rate that is tangent to the efficient frontier of risky securities.

For a two-security portfolio, which statement about portfolio variance and correlation is true according to the answer key?

III only (per the official key). — Caution: your notes say statement II may also be mathematically true. Check the original wording before relying on this one.

What are efficient portfolios of N risky securities?

Portfolios that offer the highest expected return for a given level of risk.

Which statement about selecting a portfolio on the CAL is FALSE?

That less risk-averse investors invest more in the risk-free asset. (False: they invest LESS in the risk-free asset.)

Two perfectly negatively correlated securities: A has a 16% SD, B has a 12% SD. What are the weights of A and B in the global minimum-variance portfolio?

A 0.43; B 0.57. — wA = σB / (σA + σB) = 12 / (16 + 12) = 0.43; wB = 0.57.

Optimal risky portfolio expected return 6%, SD 23%, risk-free rate 3%. What is the slope of the CAL?

0.13 — Slope = (6% − 3%) / 23% ≈ 0.13.

Markowitz portfolio theory is most concerned with what?

The effect of diversification on portfolio risk.

What risk measure is used for the Markowitz efficient frontier?

Standard deviation of returns.

Which statistic measures how the returns of two risky assets move together?

Both covariance and correlation.

What designates an individual investor's optimal portfolio?

The point of tangency between the investor's indifference curve and the CAL.

What correlation coefficient is preferred when forming a two-stock portfolio?

−1.00 (perfect negative correlation).

What is the line showing all return/SD combinations available from two assets called?

The portfolio opportunity set.

Optimal risky portfolio expected return 20%, SD 24%, risk-free rate 7%. What is the slope of the CAL?

0.54 — Slope = (20% − 7%) / 24% ≈ 0.54.

As diversification increases, total portfolio variance approaches what?

The variance of the market portfolio.

As diversification increases, unsystematic (firm-specific) portfolio risk approaches what?

0

Who first suggested the index model?

William Sharpe.

In the single-index model, what is used as the proxy for systematic risk?

A market index such as the S&P 500.

According to the index model, what drives covariances among pairs of stocks?

One common market factor; covariances are usually positive.

In the single-index model regression of a stock, what does the slope estimate?

The stock's beta.

In a factor model, stock returns relate to what kinds of events?

Both firm-specific and macroeconomic events.

For a 150-stock mean-variance (Markowitz) analysis without an index structure, how many expected returns and variances must you estimate?

150 expected returns and 150 variances.

Alpha 2%, market return 16%, risk-free rate 5%, stock excess return 11%, no firm-specific shock. What is the stock's beta?

0.82 — β = (11% − 2%) / (16% − 5%) ≈ 0.82.

Beta evolves as βt = 0.36 + 0.85 βt−1. If last year's beta was 0.60, what is the forecast beta?

0.87 — 0.36 + 0.85(0.60) = 0.87.

Index regression: estimated excess return 6%, beta 0.5, market excess return 12%. What is alpha?

0% — Alpha = 6% − 0.5(12%) = 0%.

What are the benefits of the single-index model?

It reduces the number of Markowitz calculations and separates systematic from nonsystematic risk.

Why do covariances between security returns tend to be positive?

Common economic forces affect the fortunes of many firms.

In the single-index model ri = E(ri) + βiF + ei, what does ei represent?

The impact of unanticipated firm-specific events.

According to the CAPM, a well-diversified portfolio's rate of return is a function of what?

Market risk. — In a diversified portfolio, only market (systematic) risk remains, and it is the only risk the CAPM prices.

What is the beta of the market portfolio?

1 — The market portfolio's beta is 1 by definition.

Which pricing models stipulate a relationship between expected return and risk?

Both the CAPM and APT.

Which form of the EMH says prices reflect all historical prices and current public information, but not insider information?

The semistrong form.

What do proponents of the EMH typically advocate?

A passive investment strategy, such as investing in an index fund.

Which form of the EMH says prices reflect only market trading data (past prices, trading volume, short interest)?

The weak form.

Which form of the EMH says prices reflect all information, including information available only to insiders?

The strong form.