Question 1

What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?
A) 3.72%
B) 4.23%
C) 4.74%
D) 4.90%

Accepted Answer

Return = (1.03 × 1.04 × 1.05 × 1.07)^.25 - 1 = .0474

Question 2

What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?
A) 8%
B) 8.33 %
C) 8.47%
D) 8.5 %

Accepted Answer

Return = (1.05 × 1.08 × 1.09 × 1.12)^.25- 1 = .0847

Question 3

The return on the risky portfolio is 15%. The risk-free rate, as well as the investor's borrowing rate, is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is ________.
A) 6%
B) 8.75 %
C) 10%
D) 16.25%

Accepted Answer

σ_c = y × σp = .25 σ_c = y × .20 = .25 y = .25/.20 = 1.25 1 − y = −.25 E(r_c) = 1.25 × 15% − .25 × 10% = 16.25%

Question 4

According to historical data, over the long run which of the following assets has the best chance to provide the best after-inflation, after-tax rate of return?
A) long-term Treasury bonds
B) corporate bonds
C) common stocks
D) preferred stocks

Accepted Answer

Over the long run, common stocks have provided the best after-inflation, after-tax rate of return compared to other assets such as long-term Treasury bonds, corporate bonds, and preferred stocks. However, it is important to note that common stocks also carry higher risk compared to the other assets mentioned.

Question 5

A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%. The probability of getting a return between -28% and 64% in any one year is ________.
A) 68.26%
B) 95.44%
C) 99.74%
D) 100%

Accepted Answer

Note that the expected return minus 2 standard deviations is 18% - (2 × 23%) = -28% and the expected return plus 2 standard deviations is 18% + (2 × 23%) = 64%. The probability of a return falling within ± 2 standard deviations is 95.44%.

Question 6

Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?
A) money market fund
B) U.S. T-bill
C) short-term corporate bonds
D) U.S. T-bill whose return was indexed to inflation

Accepted Answer

A U.S. T-bill whose return is indexed to inflation would be considered a risk-free asset in real terms because its return would be adjusted to keep pace with inflation, thereby protecting the purchasing power of the investment. The other options (money market funds, U.S. T-bills, and short-term corporate bonds) may be considered risk-free in nominal terms but may not provide the same level of protection against inflation.

Question 7

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 11%, you should invest ________ of your complete portfolio in Treasury bills.
A) 19%
B) 25%
C) 36%
D) 50%

Accepted Answer

.11 = W_f (.05) + (1 − W_f)[(.6)(.14) + (.4)(.10)] W_f = .19

Question 8

You invest all of your money in 1-year T-bills. Which of the following statements is (are) correct?
I. Your nominal return on the T-bills is riskless.
II. Your real return on the T-bills is riskless.
III. Your nominal Sharpe ratio is zero.
A) I only
B) I and III only
C) II only
D) I, II, and III

Accepted Answer

The nominal return on T-bills is riskless because they are backed by the government. However, the real return is not riskless due to inflation risk. The nominal Sharpe ratio is zero because T-bills have no risk premium.

Question 9

The price of a stock is $38 at the beginning of the year and $41 at the end of the year. If the stock paid a $2.50 dividend, what is the holding-period return for the year?
A) 6.58%
B) 8.86%
C) 14.47%
D) 18.66%

Accepted Answer

HPR = (41 - 38 + 2.50)/38 = .1447

Question 10

The Manhawkin Fund has an expected return of 16% and a standard deviation of 20%. The risk-free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund?
A) .8
B) .6
C) 9
D) 1

Accepted Answer

(16 - 4)/20 = .6

Question 11

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. The dollar values of your positions in X, Y, and Treasury bills would be ________, ________, and ________, respectively, if you decide to hold a complete portfolio that has an expected return of 8%.
A) $162; $595; $243
B) $243; $162; $595
C) $595; $162; $243
D) $595; $243; $162

Accepted Answer

.08(1,000) = F(.05) + (1,000 − F)[.6(.14) + .4(.10)]
F = 595
X = (1,000 − 595)(.6) = 243
Y = (1,000 − 595)(.4) = 162

Question 12

The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year?
A) -3.64%
B) -6.36%
C) -6.44%
D) -11.74%

Accepted Answer

Nominal return on stock: (50 + 3)/55 - 1 = -3.64%
Real return: (1 + R) = (1 + r)(1 + i)
1 + r = (1 - .0364)/(1.03) = .935
R = .935 - 1 = -.0644

Question 13

If the nominal rate of return on investment is 6% and inflation is 2% over a holding period, what is the real rate of return on this investment?
A) 3.92%
B) 4%
C) 4.12%
D) 6%

Accepted Answer

1 + r = (1 + R)/(1 + i) - 1
1 + r = 1.06/1.02 - 1 = .0392

Question 14

The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?
A) .50%
B) 5%
C) 6%
D) 6.5%

Accepted Answer

APR = .5% × 12 = 6%

Question 15

You have the following rates of return for a risky portfolio for several recent years:
2013 35.23%
2014 18.67%
2015 −9.87%
2016 23.45%
If you invested $1,000 at the beginning of 2013, your investment at the end of 2016 would be worth ________.
A) $2,176.60
B) $1,785.56
C) $1,645.53
D) $1,247.87

Accepted Answer

$1,000(1.3523)(1.1867)(1 + -.0987)(1.2345) = $1,785.56

Question 16

A loan for a new car costs the borrower .8% per month. What is the EAR?
A) .80%
B) 6.87%
C) 9.6%
D) 10.03%

Accepted Answer

1.00812 - 1 = 10.03%

Question 17

You have the following rates of return for a risky portfolio for several recent years:
2013 35.23%
2014 18.67%
2015 −9.87%
2016 23.45%
The annualized (geometric) average return on this investment is ________.
A) 16.15%
B) 16.87%
C) 21.32%
D) 15.60%

Accepted Answer

(1.78556)^(1/4) = 1.156 1.156 - 1 = 15.6%

Question 18

From 1926 to 2013 the world stock portfolio offered ________ return and ________ volatility than the portfolio of large U.S. stocks.
A) lower; higher
B) lower; lower
C) higher; lower
D) higher; higher

Accepted Answer

The answer of From 1926 to 2013 the world stock...

Question 19

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately ________ in the risky portfolio. This will mean you will also invest approximately ________ and ________ of your complete portfolio in security X and Y, respectively.
A) 0%; 60%; 40%
B) 25%; 45%; 30%
C) 40%; 24%; 16%
D) 50%; 30%; 20%

Accepted Answer

E(r_p) = .6(14) + .4(10) = 12.4% .08 = w_rp(.124) + (1 - w_rp)(.05) w_rp ≈ 40% w_x in complete portfolio = .40(.60) = 24% w_y in complete portfolio = .40(.40) = 16%

Question 20

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. If you decide to hold 25% of your complete portfolio in the risky portfolio and 75% in the Treasury bills, then the dollar values of your positions in X and Y, respectively, would be ________ and ________.
A) $300; $450
B) $150; $100
C) $100; $150
D) $450; $300

Accepted Answer

X = 1,000(.25)(.6) = 150
Y = 1,000(.25)(.4) = 100

Quiz 5: Risk, Return, and the Historical Record

What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?

What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?

The return on the risky portfolio is 15%. The risk-free rate, as well as the investor's borrowing rate, is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is ________.

According to historical data, over the long run which of the following assets has the best chance to provide the best after-inflation, after-tax rate of return?

A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%. The probability of getting a return between -28% and 64% in any one year is ________.

Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?

You invest all of your money in 1-year T-bills. Which of the following statements is (are) correct? I. Your nominal return on the T-bills is riskless. II. Your real return on the T-bills is riskless. III. Your nominal Sharpe ratio is zero.

The price of a stock is $38 at the beginning of the year and $41 at the end of the year. If the stock paid a $2.50 dividend, what is the holding-period return for the year?

The Manhawkin Fund has an expected return of 16% and a standard deviation of 20%. The risk-free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund?

The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year?

If the nominal rate of return on investment is 6% and inflation is 2% over a holding period, what is the real rate of return on this investment?

The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?

You have the following rates of return for a risky portfolio for several recent years: 2013 35.23% 2014 18.67% 2015 −9.87% 2016 23.45% If you invested $1,000 at the beginning of 2013, your investment at the end of 2016 would be worth ________.

A loan for a new car costs the borrower .8% per month. What is the EAR?

You have the following rates of return for a risky portfolio for several recent years: 2013 35.23% 2014 18.67% 2015 −9.87% 2016 23.45% The annualized (geometric) average return on this investment is ________.

From 1926 to 2013 the world stock portfolio offered return and volatility than the portfolio of large U.S. stocks.