fina 4011 study sheet

Which of the following statements about the implications of CAPM are FALSE? Investors will mix the optimal risky portfolio with the risk-free assets according to their risk-aversion In theory, the optimal risky portfolio is always the market portfolio Investors will have the same efficient frontier Optimal risky portfolio for each investors is different

Optimal risky portfolio for each investors is different

Which of the following statements is a TRUE statement about skewness?

Payoff from lottery follows positively skewed distribution

Which of the following is not a source of systematic risk?

Personnel Changes

You purchased a share of a stock at $25 per share. A year later, after receiving cash dividend of $2, you sold your share at $20 per share. What is your HPR?

Profit from investment = $20 − $25 + $2 = −$3 Initial investment = $25 HPR = −$3 / $25 = −0.12 (or 12%)

Which of the following statements is TRUE if 1% VaR of S&P500 index return is -10%?

There is 1% chance that S&P 500 index return falls below -10%

According to the CAPM, stocks are supposed to have __________. a) zero betas b) positive alphas c) positive betas d) zero alphas

Zero Alphas

When you invest money in a bank account, for example, you are typically quoted a __________. This is the rate at which the dollar value of your account grows.

nominal interest rate

The __________ is central to the theory and practice of investments. It has symmetric bell shaped distribution. The distribution is determined by only two parameters: mean and standard deviation

normal distribution

Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?

A portfolio with expected return of 9% and standard deviation of 21%

Which of the following statements about the single factor model is FALSE? We can estimate the single factor model by regressing excess stock return on excess market return It implies that the market return explains a part of stock return Alpha is a market premium Expectation of firm-specific return is always zero

Alpha is a market premium

The CAPM suggests that the alphas of stocks, in theory, should be __________. always zero mostly zero positive negative

Always zero

In the context of the CAPM, the measure of risk that is relevant to expected return is __________. a) unique risk b) variance of stock returns c) beta d) standard deviation of stock returns

Beta

Stock A has a beta of 1.2, and stock B has a beta of 1. The returns of stock A are __________ sensitive to changes in the market than are the returns of stock B. a) 1.2% less b) 1.2% more c) 20% more d) 20% less

C) 20% More

The __________ is the covariance divided by the product of the standard deviations of the returns on each stock.

Correlation

The index model has been estimated for stocks A and B with the following results:RA=1.5%+0.7RM+eA (R-square=0.5)RB=−1%+1.3RM+eB (R-square=0.7)E(RM)=10%, σM=15%What is the covariance between stocks A and B? a) 0.020475 b) 204.75 c) 0.91 d) 0.1431

Cov(RA,RB)=βAβBσM2 =(0.7)(1.3)(0.15)2 =0.020475

The index model has been estimated for stocks A and B with the following results:RA=1.5%+0.7RM+eA (R-square=0.5)RB=−1%+1.3RM+eB (R-square=0.7)E(RM)=10%, σM=15%, σA=14.85%, σB=23.31%What is the correlation between stocks A and B? a) 0.1431 b) 59.15 c) 0.5915 d) 0.020475

Cov(RA,RB)=βAβBσM2=(0.7)(1.3)(0.15)2=0.020475 ρA,B=Cov(RA,RB) / (σAσB) = 0.020475 / (0.1485×0.2331) = 0.5915

The index model has been estimated for stocks A and B with the following results: RA=1%+1.2RM+eA (R-square=0.3) RB=−2%+0.5RM+eB (R-square=0.2) E(RM)=10%, σM=20%, σA=43.82%, σB=22.36% What is the correlation between stocks A and B?

Cov(RA,RB)=βAβBσM2=(1.2)(0.5)(0.2)2=0.024 ρA,B=Cov(RA,RB) / (σAσB) = 0.024/ (0.4382×0.2236) = 0.2449

The security characteristic line (SCL) __________. a) plots the excess return on a security as a function of the excess return on the market b) allows one to estimate the beta of the security c) allows one to estimate the alpha of the security d) All of the above

D

The index model has been estimated for stocks A and B with the following results:RA=1.5%+0.7RM+eA (R-square=0.5)RB=−1%+1.3RM+eB (R-square=0.7)E(RM)=10%, σM=15%What are the expected excess returns of stocks A and B? a) A: 1.5% / B: −1% b) A: 7% / B: 13% c) A: 12% / B: 8.5% d) A: 8.5% / B: 12%

E(RA)=1.5%+0.7E(RM) Therefore, E(RA)=1.5%+0.7(10%)=8.5% E(RB)=−1%+1.3E(RM) Therefore, E(RB)=−1%+1.3(10%)=12%

Consider the CAPM. The market degree of risk aversion, A, is 3. The variance of the market portfolio return is 0.0225. What is the expected excess return on the market portfolio? 2.25% 6.75% 45% 10.75%

E(RM)=A×σM^2 A=3 and σM2=0.0225 Therefore, E(RM) = 3 x 0.0225 = 0.0675 (or 6.75%)

You put half of your money in a stock that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in another stock that has an expected return of 6% and a standard deviation of 12%. The two stocks have a correlation of 0.55. What is the expected return of the resulting portfolio?

E(rA)=0.14; σA=0.24; wA=0.5 E(rB)=0.06; σB=0.12; wB=0.5 ρA,B=0.55 Expected return of the portfolio = E(rP) =wAE(rA)+wBE(rB) =(0.5)(0.14)+(0.5)(0.06) =0.1 (or 10%)

You put half of your money in a stock that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in another stock that has an expected return of 6% and a standard deviation of 12%. The two stocks have a correlation of 0.55. What is the standard deviation of the resulting portfolio?

E(rA)=0.14; σA=0.24; wA=0.5 E(rB)=0.06; σB=0.12; wB=0.5 ρA,B=0.55 Variance of the portfolio = σP2 =(wA)2(σA)2+(wB)2(σB)2+2(wA)(wB)(σA)(σB)(ρA,B) =(0.5)2(0.24)2+(0.5)2(0.12)2+2(0.5)(0.5)(0.24)(0.12)(0.55) =0.02592 Standard deviation of the portfolio = square root of 0.02592 = 0.1610 or (16.1%)

You put 30% of your money in stock A that has an expected return of 10% and a standard deviation of 20%. You put the rest of your money in another stock B that has an expected return of 15% and a standard deviation of 15%. The two stocks have a correlation of 0.2. What is the standard deviation of the resulting portfolio?

E(rA)=0.1; σA=0.2; wA=0.3E(rB)=0.15; σB=0.15; wB=0.7 ρA,B=0.2 Variance of the portfolio = σP2 =(wA)2(σA)2+(wB)2(σB)2+2(wA)(wB)(σA)(σB)(ρA,B) =(0.3)2(0.2)2+(0.7)2(0.15)2+2(0.3)(0.7)(0.2)(0.15)(0.2) =0.017145 Standard deviation of the portfolio = square root of 0.017145= 0.1309 or (13.09%)

Which of the following statements about separation property FALSE?

Every investor chooses the same point on CAL constructed from a risk-free asset and an optimal risky portfolio

The standard deviation of the return on the market portfolio is 0.2 and the expected excess market return is 10%. What is the market degree of risk aversion, A?

Expected excess market return = Risk Aversion x Variance of Market Index E(RM)=A×σM2 The question states that E(RM)=10% and σM=0.2 Therefore 0.1=A×0.04 A=2.5

An investor can design a complete portfolio based on a risky portfolio and a risk-free asset. The risky portfolio has an expected return of 10% and a standard deviation of 20%. Risk-free rate is 5%. If the investment weight on the risky portfolio is 70% and the weight on the risk-free asset is 30%, what is expected return and standard deviation of the complete portfolio?

Expected return of the complete portfolio =wP×E(rP)+wf×rf = 0.7×0.1+0.3×0.05 =0.085 (or 8.5%) Standard deviation of the complete portfolio=wP×σP=0.7×0.2 =0.14 (or 14%)

Kevin's stock portfolio earned 5% return in the past three months. What is the annual percentage rate (APR) of the portfolio return?

HPR = 5% per 3 months N = 4 APR = HPR × N = 5% × 4 = 20%

Convert 3-month HPR of 5% into effective annual rate (EAR)

HPR = 5% per 3 months N = 4 EAR= (1+HPR)N − 1 = 1.054 − 1 = 0.2155 (or 21.55%)

You are constructing a scatter plot of excess returns for stock A versus the market index. If the correlation coefficient between stock A and the index is -0.5, you will find that the line of best fit has a ________.

Negative Slope

Which of the following is NOT an assumption of CAPM? Investors' planning horizon is a single period Investors have different input lists There are no taxes Investors are rational, mean-variance optimizers

Investors have different input lists

Which of the following statements about optimal risky portfolio is FALSE?

It is a portfolio that minimizes standard deviation

Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is __________.

Less than 1

The index model has been estimated for stocks A and B with the following results:RA=1.5%+0.7RM+eA (R-square=0.5)RB=−1%+1.3RM+eB (R-square=0.7)E(RM)=10%, σM=15%What are the standard deviations of stocks A and B's residuals, eA and eB? a) A: 10.5% / B: 12.8% b) A: 14.85% / B: 23.3% c) A: 12.8% / B: 10.5% d) A: 15% / B: 15%

R-square=(βA2σM2 )/(σA2) gives 0.5 ((0.7)2(0.15)2)/(σA2) Solving the equation gives σA2=0.02205 σA2=βA2σM2+σ(eA)2 gives 0.02205=(0.7)2(0.15)2+σ(eA)2 Therefore, σ(eA)2=0.011025 σ(eA)=0.105 (or 10.5%) Stock B: R-square=(βB2σM2 )/(σB2) gives 0.7=((1.3)2(0.15)2)/(σB2) Solving the equation gives σB2=0.054321 σB2=βB2σM2+σ(eB)2 gives 0.054321=(1.3)2(0.15)2+σ(eB)2 Therefore, σ(eB)2=0.016296 σ(eB)=0.128 (or 12.8%)

Which of the following is a different type of risk? Firm-specific risk Systematic risk Unique risk Diversifiable risk

SYstematic risk

If a portfolio had a return of 8%, the risk-free asset return was 3%, and the standard deviation of the portfolio's excess returns was 20%, the Sharpe measure would be __________.

Sharpe ratio = ( E(rp) − rf ) / σp = (8% − 3%) / 20% = 0.25

BBY's expected annual return is 10% and its standard deviation is 20%. If the risk-free rate is 3%, what is Sharpe ratio of BBY?

Sharpe ratio = (expected stock return − risk free rate) / standard deviation = ( 10% − 3% ) / 20% = 0.35

The index model has been estimated for stocks A and B with the following results: RA=1%+1.2RM+eA (R-square=0.3) RB=−2%+0.5RM+eB (R-square=0.2) E(RM)=10%, σM=20% What are the standard deviations of stocks A and B returns?

Stock A: R-square=(βA2σM2 )/(σA2) gives 0.3=((1.2)2(0.20)2)/(σA2) Solving the equation gives σA2=0.192 Therefore σA=0.4382 Stock B: R-square=(βB2σM2 )/(σB2) gives 0.2=((0.5)2(0.20)2)/(σB2) Solving the equation gives σB2=0.05 Therefore, σB=0.2236

The index model has been estimated for stocks A and B with the following results:RA=1.5%+0.7RM+eA (R-square=0.5)RB=−1%+1.3RM+eB (R-square=0.7)E(RM)=10%, σM=15%What are the standard deviations of stocks A and B returns? a) A: 10.5% / B: 12.8% b) A: 15% / B: 15% c) A: 14.85% / B: 23.31% d) A: 12.8% / B: 10.5%

Stock A: R-square=(βA2σM2 )/(σA2) gives 0.5 ((0.7)2(0.15)2)/(σA2) Solving the equation gives σA2=0.02205 Therefore σA=0.1485 Stock B: R-square=(βB2σM2 )/(σB2) gives 0.7=((1.3)2(0.15)2)/(σB2) Solving the equation gives σB2=0.054321 Therefore, σB=0.2331

Suppose that you have the following two opportunities from which to construct a complete portfolio: risk-free asset earning 2%, and a risky asset with expected return of 12% and standard deviation of 20%. If you construct a complete portfolio that has expected return of 5%, what is its standard deviation?

Suppose the weight on the risky asset is w and weight on the risk-free asset is 1−w. The expected return of the complete portfolio is w×(12%)+(1−w)×(2%)=2%+w×(10%) Solving 2%+w×(10%)=5% gives w=0.3 The standard deviation of the complete portfolio is w×(20%)=6% The answer is 6%

Suppose that you have the following two opportunities from which to construct a complete portfolio: risk-free asset earning 2%, and a risky asset with expected return of 12% and standard deviation of 20%. If you construct a complete portfolio that has standard deviation of 12%, what is its expected return?

Suppose the weight on the risky asset is w and weight on the risk-free asset is 1−w. The standard deviation of the complete portfolio is w×(20%) Solving w×(20%)=12% gives w=0.6 The expected return of the complete portfolio is w×(12%)+(1−w)×(2%)=2%+w×(10%) =8% The answer is 8%

Suppose that you have the following two opportunities from which to construct a complete portfolio: risk-free asset earning 1%, and a risky asset with expected return of 11% and standard deviation of 30%. If you construct a complete portfolio that has standard deviation of 12%, what is its expected return?

Suppose the weight on the risky asset is w and weight on the risk-free asset is 1−w. The standard deviation of the complete portfolio is w×(30%) Solving w×(30%)=12% gives w=0.4 The expected return of the complete portfolio is w×(11%)+(1−w)×(1%)=1%+w×(10%) =5% The answer is 5%

Which of the following provides the best example of a systematic-risk event?

The Federal Reserve increases interest rates 50 basis points.

Based on the scenarios in the following table, choose which of the following statements below are correct?

The correlation between stock A and stock B is negative

Which of the following statements about beta is FALSE? It measures systematic risk Defensive stocks usually have betas less than 1 It is the slope of the SCL The market portfolio has zero beta

The market portfolio has zero beta

The expected firm-specific return is __________.

always zero

Most interest rates are quoted as __________, which annualize per-period rates using a simple interest approach, ignoring compound interest.

annual percentage rates

Analysts may use regression analysis to estimate the index model for a stock. When doing so, the intercept of the regression line is an estimate of __________. a) the beta of the stock b) the standard deviation of the stock c) the alpha of the stock d) the expected return of the stock

c) the alpha of the stock

The probability distribution lets us derive measurements for both the reward and the risk of the investment. The reward from the investment is its __________, which you can think of as the average HPR you would earn if you were to repeat an investment in the asset many times.

expected return

Published data on past returns earned by mutual funds are required to be __________

geometric average returns

The portfolio with the lowest standard deviation for any expected return is called the __________.

global minimum variance portfolio

The capital allocation line can be described as the __________.

investment opportunity set formed with a risky asset and a risk-free asset

On a standard risk-return space, investors will prefer portfolios that lie to the __________ the current investment opportunity set.

left and above

The efficient frontier represents a set of portfolios that __________.

maximize expected return for a given level of risk

The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two risky assets is called the __________.

portfolio opportunity set

The unsystematic risk of a specific security __________

results from factors unique to the firm

If you are promised a nominal return of 12% on a 1-year investment, and you expect the inflation rate to be 3%, what real rate of return do you expect to earn? Use the exact formula.

rreal = (rnorm − i ) / ( 1 + i )=(0.12 − 0.03) / (1 + 0.03) rnorm=nominal rate of return i=inflation rate Rreal=real rate of return

If you are promised a nominal return of 12% on a 1-year investment, and you expect the inflation rate to be 3%, what real rate of return do you expect to earn? Use the approximation.

rreal ≈ (rnorm − i ) = (0.12 − 0.03) = 0.09 rnorm=nominal rate of return i=inflation rate Rreal=real rate of return

Over the past year you earned a nominal rate of interest of 10% on your money. The inflation rate was 5% over the same period. What is the exact real rate of return on your investment?

rreal=(rnom − i) / (1 + i) = (0.10 − 0.05) / (1 + 0.05) = 0.0476

Other things equal, diversification is most effective when __________

securities' returns are negatively correlated

Historical records regarding return on stocks, Treasury bonds, and Treasury bills from 1927 to 2016 show that __________.

stocks offered investors greater rates of return than bonds and bills

Roll's critique suggests that __________. even without a good measure of the market portfolio, the theory holds the market portfolio should not include illiquid assets such as real estate S&P500 index is a good proxy for the market portfolio the market portfolio cannot be observed

the market portfolio cannot be observed

In words, the real rate of interest is approximately equal to __________.

the nominal rate minus the inflation rate

The security characteristic line (SCL) associated with the single-index model is a plot of __________.

the security's excess returns on the vertical axis and the market index's excess returns on the horizontal axis.

The expected rate of return of a portfolio of risky securities is __________

the weighted sum of the securities' expected returns