Question 1

What is the amount of the risk premium on a U.S. Treasury bill if the risk-free rate is 3.1 percent, the inflation rate is 2.6 percent, and the market rate of return is 7.4 percent?

Accepted Answer

The risk premium on a U.S. Treasury bill is 0 percent because Treasury bills are considered risk-free securities. The risk-free rate already accounts for the inflation rate, so no additional risk premium is needed.

Question 2

The common stock of Air Express had annual returns of 11.7 percent, 8.8 percent, 16.7 percent, and −7.9 percent over the last four years, respectively. What is the standard deviation of these returns?

Accepted Answer

The answer of The common stock of Air Express had...

Question 3

Suppose a stock had an initial price of $76 per share, paid a dividend of $1.42 per share during the year, and had an ending share price of $81. What was the capital gains yield?

Accepted Answer

Capital gains yield = (ending share price - initial share price) / initial share price

= ($81 - $76) / $76

= $5 / $76

= 0.0658 or 6.58% (rounded to two decimal places)

Therefore, the capital gains yield is 6.58%, and the best choice is D.

Question 4

Leo purchased a stock for $63.80 a share, received a dividend of $2.68 a share and sold the shares for $59.74 each. During the time he owned the stock, inflation averaged 2.8 percent. What is his approximate real rate of return on this investment?

Accepted Answer

Leo's nominal return is calculated as: ((59.74 + 2.68 - 63.80) / 63.80) * 100 = -6.38%. To find the real rate of return, adjust for inflation: Real return ≈ Nominal return - Inflation rate = -6.38% - 2.8% = -9.18%. However, using the formula for real return: (1 + nominal return) / (1 + inflation rate) - 1, we get: (1 - 0.0638) / (1 + 0.028) - 1 ≈ -4.96%.

Question 5

You bought one of Shark Repellant's 6 percent coupon bonds one year ago for $867. These bonds pay annual payments, have a face value of $1,000, and mature 12 years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 7.4 percent. The inflation rate over the past year was 2.9 percent. What was your total real return on this investment?

Accepted Answer

First, we need to calculate the coupon payment: 
Coupon payment = Face value x Coupon rate = $1,000 x 6% = $60

Next, we need to calculate the selling price of the bond today: 
PV = Coupon payment x (1 - (1 + r)^-n) / r + Face value / (1 + r)^n 
PV = $60 x (1 - (1 + 0.074)^-12) / 0.074 + $1,000 / (1 + 0.074)^12 
PV = $907.24

The total real return is the nominal return minus the inflation rate: 
Total real return = (Selling price + Coupon payment received) / Initial investment - 1 - Inflation rate 
Total real return = ($907.24 + $60) / $867 - 1 - 0.029 
Total real return = 0.0661 or 6.61%

Therefore, the answer is B.

Question 6

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 7 percent, 13 percent, 19 percent, −8 percent, and 15 percent. Suppose the average inflation rate over this time period was 2.6 percent and the average T-bill rate was 3.1 percent. Based on this information, what was the average nominal risk premium?

Accepted Answer

The answer of You've observed the following returns on Crash-n-Burn...

Question 7

Today, you sold 540 shares of stock and realized a total return of 7.3 percent. You purchased the shares one year ago at a price of $24 a share and have received a total of $86 in dividends. What is your capital gains yield on this investment?

Accepted Answer

The answer of Today, you sold 540 shares of stock...

Question 8

One year ago, you purchased 100 shares of Best Wings stock at a price of $38.19 a share. The company pays an annual dividend of $.46 per share. Today, you sold for the shares for $37.92 a share. What is your total percentage return on this investment?

Accepted Answer

The answer of One year ago, you purchased 100 shares...

Question 9

A stock had annual returns of 11.3 percent, 9.8 percent, −7.3 percent, and 14.6 percent for the past four years. Based on this information, what is the 95 percent probability range of returns for any one given year?

Accepted Answer

To find the 95% probability range of returns for any one given year, we first calculate the mean and standard deviation of the annual returns. The returns are 11.3%, 9.8%, -7.3%, and 14.6%.Mean = (11.3 + 9.8 - 7.3 + 14.6) / 4 = 28.4 / 4 = 7.1%To calculate the standard deviation, we first find the variance:Variance = [(11.3 - 7.1)^2 + (9.8 - 7.1)^2 + (-7.3 - 7.1)^2 + (14.6 - 7.1)^2] / 4= [(4.2)^2 + (2.7)^2 + (-14.4)^2 + (7.5)^2] / 4= [17.64 + 7.29 + 207.36 + 56.25] / 4= 288.54 / 4 = 72.135Standard deviation = sqrt(72.135) ≈ 8.49%For a 95% probability range (assuming a normal distribution), we use the mean ± 2 standard deviations:Lower bound = 7.1% - 2(8.49%) = 7.1% - 16.98% = -9.88%Upper bound = 7.1% + 2(8.49%) = 7.1% + 16.98% = 24.08%While the calculated bounds do not exactly match any of the options, the closest match and the principle of using mean ± 2 standard deviations for a 95% confidence interval suggest that the correct answer should reflect a range that encompasses the mean with a margin that is roughly twice the standard deviation on either side. The provided options do not directly align with the calculated values due to potential rounding or calculation differences, but the approach typically involves finding the mean and standard deviation, then applying the concept of a 95% confidence interval with mean ± 2 standard deviations. Given the options, C) −12.5 to 26.7 percent is the closest to representing a reasonable range based on the standard deviation approach, despite the mismatch in exact numbers, suggesting a possible simplification or estimation in the question or answer choices.

Question 10

Aimee is the owner of a stock with annual returns of 17.6 percent, −11.7 percent, 5.6 percent, and 9.7 percent for the past four years. She thinks the stock may achieve a return of 17 percent again this coming year. What is the probability that your friend is correct?

Accepted Answer

There is no statistical basis to determine the probability of achieving a specific return like 17% based on past returns alone. The probability is subjective and could be considered greater than 16% if Aimee has additional information or confidence in her prediction.

Question 11

Suppose you bought a $1,000 face value bond with a coupon rate of 5.6 percent one year ago. The purchase price was $987.50. You sold the bond today for $994.20. If the inflation rate last year was 2.6 percent, what was your exact real rate of return on this investment?

Accepted Answer

The real rate of return can be calculated using the formula for the exact real return, which is (1 + nominal return) / (1 + inflation rate) - 1. First, calculate the nominal return: you received $56 (5.6% of $1000) in coupon payments and had a capital gain of $6.70 ($994.20 - $987.50). So, the total return is $62.70. The nominal return is $62.70 / $987.50 = 0.0635 or 6.35%. Using the inflation rate of 2.6% or 0.026, the exact real return is (1 + 0.0635) / (1 + 0.026) - 1 = 1.0635 / 1.026 - 1 ≈ 0.0365 or 3.65%.

Question 12

A stock had returns of 3 percent, 12 percent, 26 percent, −14 percent, and −1 percent for the past five years. Based on these returns, what is the approximate probability that this stock will return at least 20 percent in any one given year?

Accepted Answer

The stock returned at least 20 percent in 1 out of 5 years (26 percent in the third year), so the approximate probability is 1/5 or 20 percent. However, the closest option provided is 16 percent, making E the best choice.

Question 13

Christina purchased 500 shares of stock at a price of $62.30 a share and sold the shares for $64.25 each. She also received $738 in dividends. If the inflation rate was 3.9 percent, what was her exact real rate of return on this investment?

Accepted Answer

The answer of Christina purchased 500 shares of stock at...

Question 14

A stock had annual returns of 5.3 percent, −2.7 percent, 16.2 percent, and 13.6 percent over the past four years. Which one of the following best describes the probability that this stock will produce a return of 20 percent or more in a single year?

Accepted Answer

Given the annual returns listed, there is no direct way to calculate the exact probability of achieving a 20 percent return in a future year without more statistical data. However, we can infer that since one of the years had a return close to 20 percent (16.2 percent), the probability of achieving a 20 percent return is not impossible or extremely low. Therefore, the best estimate with the given options is that the probability is less than 16 percent but more than 2.5 percent, acknowledging the variability in the stock's performance without assuming an extremely high or low likelihood based on the provided returns.

Question 15

You find a certain stock that had returns of 8 percent, −3 percent, 12 percent, and 17 percent for four of the last five years. The average return of the stock for the past five-year period was 6 percent. What is the standard deviation of the stock's returns for the five-year period?

Accepted Answer

The answer of You find a certain stock that had...

Question 16

A stock had returns of 14 percent, 13 percent, −10 percent, and 7 percent for the past four years. Which one of the following best describes the probability that this stock will lose no more than 10 percent in any one year?

Accepted Answer

Given the returns for the past four years, the stock lost more than 10 percent in only one year (-10 percent). Therefore, in 3 out of 4 years, the stock did not lose more than 10 percent. This translates to a 75% historical probability (3 out of 4 years), which is greater than 84 percent but less than 97.5 percent when considering the choices provided.

Question 17

Last year, you purchased 400 shares of Analog stock for $12.92 a share. You have received a total of $136 in dividends and $4,301 in proceeds from selling the shares. What is your capital gains yield on this stock?

Accepted Answer

Capital gains yield is calculated as (Selling Price - Purchase Price) / Purchase Price. The purchase price was 400 shares * $12.92 = $5,168. The selling price was $4,301. The capital gain is $4,301 - $5,168 = -$867. The capital gains yield is -$867 / $5,168 = -16.78%.

Question 18

A stock has an expected rate of return of 9.8 percent and a standard deviation of 15.4 percent. Which one of the following best describes the probability that this stock will lose at least half of its value in any one given year?

Accepted Answer

The probability of a stock losing at least half of its value in any given year is extremely low, especially when the expected rate of return is positive (9.8 percent) and the standard deviation, which measures the volatility, is 15.4 percent. This indicates that while the stock's returns can vary, the likelihood of such an extreme loss is very small, hence less than .5 percent is a reasonable estimation without performing detailed statistical calculations.

Question 19

Four months ago, you purchased 900 shares of LBM stock for $7.68 a share. Last month, you received a dividend payment of $.12 a share. Today, you sold the shares for $9.13 a share. What is your total dollar return on this investment?

Accepted Answer

The total dollar return is calculated by adding the capital gain and the dividend income. The capital gain is (9.13 - 7.68) * 900 = $1,305. The dividend income is 0.12 * 900 = $108. Therefore, the total dollar return is $1,305 + $108 = $1,413.

Question 20

A stock had returns of 5 percent, 14 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns?

Accepted Answer

The answer of A stock had returns of 5 percent,...

Quiz 12: Some Lessons from Capital Market History