FIN327 Ch. 5 Quiz

A stock investor earned a 2.9% dividend yield and a 7.8% capital gain yield in a year in which inflation was 3.9%. The investor's approximate real return was ______.

rreal ~ (7.8% + 2.9%) - 3.9% ~ 6.8%

An investor earned a geometric average return over 4 years of 12.70%. The first year's return was 13.20%, the second year's return was -4.60%, the third year's return was 22.60%. What was the fourth year's return?

1.127^4 = (1.132 x (1+(-.046)) x 1.226 x (1+r); r = ( 1.61323/ 1.32399) - 1 = 21.85%

An investor earned an arithmetic average return over 4 years of 12.5%. The first year's return was 13.0%, the second year's return was -5.00%, the third year's return was 22.0%. What was the fourth year's return?

12.50% = (13.00% + -5.00% + 22.00% + r) / 4; r = (12.50% x 4) - 13.00% + 5.00% - 22.00% = 20.00%

An investor who is risk neutral would choose which one of the following investments

A risk neutral investor only cares about expected return (A = 0) so he or she would choose the stock with the greatest expected return, which is Stock D.

Annualized Holding Period Returns An investor buys a share of stock for $23.10 and holds it for four years and then sells it for $25.60. The investor collected a $2.60 per share dividend at the end of the four years. The investor's annualized HPR with compounding equals __________.

HPR = (25.60 - 23.10 + 2.60) / $23.10 = 22.08%. The annualized HPR with compounding = (1+HPR)^ (1/N), where N = number of years or 1.2208^(1/4) -1 = 5.11%.

Two years ago Bill bought three share of stock that cost $58.00. The stock paid a $2.80 dividend a year after Bill bought it and then he bought four more shares of stock for $60.00 a share. A year after this Bill collected a $3.30 per share dividend and then Bill sold all shares at $61.00. What was Bill's geometric average time weighted return?

HPR first year = ($60.00 - $58.00 + $2.80)/ $58.00 = 8.28%; HPR second year = ($61.00 - $60.00 + $3.30) / $60.00 = 7.17%; The geometric average of these returns = (1.0828 x 1.0717)^1/2 - 1 = 7.72%.

Suppose you have $7,100 invested in a stock portfolio in October. You have $3,700 invested in Stock A, $2,200 in Stock B and $1,200 in Stock C. The HPR for the month of September for Stock A was 1.3%, for Stock B the HPR was -4.05% and for Stock C the HPR was 3%. What was the average HPR for the portfolio for the month of October?

HPRavg = (0.013 x (3,700/7,100)) + (-0.0405 x (2,200/7,100)) + (0.03 x (1,200/7,100)) = -0.07%

An investor finds that the risk free rate = 2.70% when the expected return and standard deviation of a risky portfolio is 11% and 19% respectively. If the investor places 55.00% of their money in the risky portfolio and the rest in the risk free asset the resulting complete portfolio expected return is ______ and the standard deviation is ______.

If E(rC) = return for the complete portfolio then E(rC) = (0.55 × 11%) + (0.45 × 2.70%) = 7.27%. The σC = (0.55 × 19%) + (0.45 × 0%) = 10.45%.

Choice A portfolio has an excess return of 9.8% and a standard deviation of 38.4%. What is the maximum coefficient of risk aversion A that an investor could have and still choose to invest in the risky portfolio?

Maximum A = 9.8% / (0.5 × (0.384^2)) = 1.329

If stock distributions exhibit leptokurtosis then an investor should expect which one of the following?

More extreme gains and losses than the normal distribution predicts. Leptokurtosis means that the distribution has fat tails or an investor should expect to see more extreme gains and losses than predicted by the normal distribution.

Two years ago Bill bought one share of stock that cost $52. The stock paid a $2.20 dividend a year after Bill bought it and then he bought two more shares of stock for $54.00 a share. A year after this Bill collected a $2.70 per share dividend and then Bill sold all shares at $55.00. What was Bill's dollar weighted return?

Original cash flow = -$52, cash flow one year after purchase = (2 x -$54) + $2.20 = -$105.80, final cash flow = 3 x ($2.70 + 55) = $173.10. Financial Calc: CF=0 CF1= -52 CF2=-105.80 Cf3=173.10 CPT IRR

A stock had an average return of 16% when the risk free rate was 4.6%. The stock had a standard deviation of 28.4%. The stock's Sharpe ratio was _________.

Sharpe = (16% − 4.6%) / 28.4% = 0.40

From 1926 to 2008 which one of the following classes of securities had the largest excess return?

The U.S. small stocks asset class had the largest average return and excess return over this time period, followed by U.S. large stocks, World stocks and finally World bonds.

An investor has a 5.0% HPR on a 8 month investment. What is the annualized rate of return with compounding?

The annualized HPR = 1.05^(12/8) - 1 = 7.59%

The highest Sharpe ratio implied by the CML was found in which of the following periods?

The highest Sharpe ratio implied by the CML was found in the 1956-1984 time period. The return earned per unit of risk was the highest in this period.

An analyst estimates a 26% probability of a recession next year, a 50% probability of normal economic growth and a 24% probability of a strong recovery. If a recession occurs a stock is projected to have a -16.1% return. With normal growth the stock will generate a 11.1% return and if the strong recovery occurs the stock will have a 26.1% rate of return. This stock's standard deviation is _______.

The stock's expected return = (0.26 x -0.161) + (0.5 x 0.111) + (0.24 x 0.261) = 7.63%. The stock's variance = [(0.26)(-0.161 - 0.0763)^2 + (0.5)(0.111 - 0.0763)^2 + (0.24)(0.261 - 0.0763)^2] = 0.02343%2. The standard deviation is the square root of the variance so the standard deviation = 15.307%.

You put $2,400 in risk free T-Bills and $9,600 in a stock portfolio. The stock portfolio is invested as follows: In Stock A you put $4,400, in Stock B you put $3,300 and in Stock C you put $1,900. In the complete portfolio the weights of Stock A, B and C are respectively ________________.

Wrf = $2,400/($2,400+$9,600) = 20.00%; Wrp = $9,600/($2,400+$9,600) = 80.00%; A = 80.00% × ($4,400 / $9,600) = 36.67%; B = 80.00% × ($3,300 / $9,600) = 27.50%; C. 80.00% × ($1,900 / $9,600) = 15.83%;

An investor earned a 9% nominal, pre-tax rate of return. The investor is in the 27% tax bracket and inflation was 2.30%. What was the investor's exact real, after-tax rate of return?

[[1+ (0.09 × (1 - 0.27))] / 1.0230] - 1 = 4.17%

The best measure of the compound historical return is the ____________; the best measure of the expected return is the ____________.

geometric mean; arithmetic mean. The geometric mean accounts for compounding and is the best measure of a compound historical return while the arithmetic mean is the best measure of the expected return.

$515,000 stock portfolio has an annual expected return of 11% and a standard deviation of 22%. What is the dollar portfolio VaR at a 5% probability level?

−$129,712. The VaR at a 5% probability level = Expected return + -1.64485σ = 0.11 + (-1.64485 x 0.22) = -25.19%. The dollar VaR = $515,000 x -.2519 = −$129,712