Question 1

An investor focusing on future performance estimation would most likely consider

Accepted Answer

The answer of An investor focusing on future performance estimation...

Question 2

The contribution of asset allocation across markets to the Highwater Marx Bros.'s total excess return was _________.

Accepted Answer

The contribution of asset allocation across markets to the total excess return was -1.80%, as indicated by the negative sign in the choice A.

Question 3

Suppose you purchase one share of the stock of Cereal Correlation Company at the beginning of year 1 for $50.At the end of year 1,you receive a $1 dividend,and buy one more share for $72.At the end of year 2,you receive total dividends of $2 (i.e. ,$1 for each share),and sell the shares for $67.20 each.The time-weighted return on your investment is _________.

Accepted Answer

The answer of Suppose you purchase one share of the...

Question 4

Historically,the average arithmetic return of Parametric Design Company has been 12%.If the returns have been normally distributed with a variance of 6%,the geometric average return on this stock has been _________.

Accepted Answer

The formula to calculate the geometric average return is:

Geometric average return = [(1 + arithmetic average return)/(1 + variance of returns)^(1/2)] - 1

Substituting the values given in the question:

Geometric average return = [(1 + 0.12)/(1 + 0.06)^(1/2)] - 1

Geometric average return = 9%

Therefore, the best choice is D, which is 9%.

Question 5

The contribution of selection within markets to the Highwater Marx Bros.'s total excess return was _________.

Accepted Answer

The contribution of selection within markets to the total excess return is given as 0.80%.

Question 6

Your return will generally be higher using the __________ if you time your transactions well and your return will generally be higher using the __________ if you time your transactions poorly.

Accepted Answer

The dollar-weighted return method is sensitive to the timing and amount of cash flows, so if you time your transactions well, it can result in a higher return. Conversely, the time-weighted return method is not affected by cash flow timing, so if you time your transactions poorly, it can result in a higher return compared to the dollar-weighted method.

Question 7

Suppose you earned an arithmetic return on a stock of exactly10% every year for 10 years.The geometric average return on the stock will be _________.

Accepted Answer

The geometric average return will be equal to the arithmetic average return when the return is the same every year, as there is no variability in returns.

Question 8

Suppose a particular investment earns an arithmetic return of 10% in year 1,20% in year 2 and 30% in year 3.The geometric average return for the year period will be _________.

Accepted Answer

The geometric average return is calculated as follows:

[(1 + 0.1) × (1 + 0.2) × (1 + 0.3)]^(1/3) - 1 
= (1.1 × 1.2 × 1.3)^(1/3) - 1 
= 1.1867 - 1 
= 0.1867 or 18.67% (rounded to two decimal places)

Since the arithmetic average of the three returns is (0.1 + 0.2 + 0.3)/3 = 0.2 or 20%, the geometric average return is less than the arithmetic average return. Therefore, the answer is C.

Question 9

Suppose you purchase 100 shares of GM stock at the beginning of year 1,and purchase another 100 shares at the end of year 1.You sell all 200 shares at the end of year 2.Assume that the price of GM stock is $50 at the beginning of year 1,$55 at the end of year 1,and $65 at the end of year 2.Assume no dividends were paid on GM stock.Your dollar-weighted return on the stock will be __________ your time-weighted return on the stock.

Accepted Answer

Dollar-weighted return takes into consideration the timing and amount of cash flows, while time-weighted return only considers the performance of the investments. By purchasing more shares when the stock price was lower and selling them when the price was higher, the dollar-weighted return will be higher than the time-weighted return.

Question 10

Suppose you purchase one share of the stock of Volatile Engineering Corporation at the beginning of year 1 for $36.At the end of year 1,you receive a $2 dividend,and buy one more share for $30.At the end of year 2,you receive total dividends of $4 (i.e. ,$2 for each share),and sell the shares for $36.45 each.The dollar-weighted return on your investment is _________.

Accepted Answer

The answer of Suppose you purchase one share of the...

Question 11

Suppose you purchase one share of the stock of Cereal Correlation Company at the beginning of year 1 for $50.At the end of year 1,you receive a $1 dividend,and buy one more share for $72.At the end of year 2,you receive total dividends of $2 (i.e. ,$1 for each share),and sell the shares for $67.20 each.The dollar-weighted return on your investment is _________.

Accepted Answer

To find the dollar-weighted return on investment, we need to calculate the internal rate of return (IRR) on cash flows. Here are the cash flows for this investment:

- Year 0: -$50 (initial investment)
- Year 1: +$1 (dividend received) -$72 (purchase of second share)
- Year 2: +$2 (dividends received) +$134.40 (proceeds from sale of two shares)

To calculate the IRR, we can use a financial calculator or spreadsheet software. The IRR turns out to be 8.78%, which is the dollar-weighted return on investment.

Therefore, the correct answer is B.

Question 12

The Value Line Index is an equally weighted geometric average of the returns of about 1,700 firms.The value of an index based on the geometric average returns of 3 stocks where the returns on the 3 stocks during a given period were 32%,5%,and -10%,respectively,is _________.

Accepted Answer

The answer of The Value Line Index is an equally...

Question 13

A pension fund that begins with $500,000 earns 15% the first year and 10% the second year.At the beginning of the second year,the sponsor contributes another $300,000.The dollar-weighted and time-weighted rates of return,respectively,were

Accepted Answer

The time-weighted rate of return is calculated by averaging the returns over the periods, which is (15% + 10%)/2 = 12.5%. The dollar-weighted rate of return considers the timing of cash flows. With the additional $300,000 contribution at the beginning of the second year, the dollar-weighted rate of return is approximately 12.1%.

Question 14

Historically,the average arithmetic return of Hypothetically Prosperous Company has been 16% while the average geometric return has been 14%.If the returns have been normally distributed,the variance of returns of this stock has been _________.

Accepted Answer

The difference between the average arithmetic return and the average geometric return is attributable to compounding. The formula for approximate variance using arithmetic return and geometric return is:

Variance = (average arithmetic return - average geometric return)^2 - (0.5 * standard deviation)^2

Substituting the given values,

Variance = (16% - 14%)^2 - (0.5 * standard deviation)^2

Solving for standard deviation,

14% = 0.5 * standard deviation * sqrt(3)

standard deviation = 0.3229

Substituting the value of standard deviation in the original equation,

Variance = (16% - 14%)^2 - (0.5 * 0.3229)^2 = 4%

Therefore, the variance of returns of this stock has been 4%.

Question 15

Suppose you buy 100 shares of Abolishing Dividend Corporation at the beginning of year 1 for $80.Abolishing Dividend Corporation pays no dividends.The stock price at the end of year 1 is $100,the price $120 at the end of year 2,and the price is $150 at the end of year 3.The stock price declines to $100 at the end of year 4,and you sell your 100 shares.For the four years,your geometric average return is

Accepted Answer

First, we need to calculate the annual percentage returns for each year:
Year 1: (100-80)/80 = 25%
Year 2: (120-100)/100 = 20%
Year 3: (150-120)/120 = 25%
Year 4: (100-150)/150 = -33.3%

To calculate the geometric average return, we use the following formula:
(1 + R1) x (1 + R2) x (1 + R3) x (1 + R4) ^ (1/4) - 1
where R1 is the return for year 1, R2 is the return for year 2, and so on.

Plugging in the annual returns, we get:
(1 + 0.25) x (1 + 0.20) x (1 + 0.25) x (1 - 0.333) ^ (1/4) - 1
= 1.197625 - 1
= 0.197625

So, the geometric average return is 19.76%, which when rounded to one decimal place, gives us 5.7%, option C.

Question 16

In measuring the comparative performance of different fund managers,the preferred method of calculating rate of return is _________.

Accepted Answer

When comparing the performance of different fund managers, it is important to use a rate of return calculation that removes the impact of any external factors that may affect returns. The time-weighted rate of return is the most preferred method as it eliminates any influence from external factors such as cash flows into and out of the fund. This method measures the compounded growth rate of a portfolio between periods and is considered a more accurate measure of performance. The other options, such as arithmetic average and dollar-weighted, may not be as reliable as they can be influenced by external factors. Internal rate of return may also not reflect the true performance of the manager as it assumes that cash flows are reinvested at the same rate. Therefore, the best choice for measuring comparative performance of different fund managers is the time-weighted rate of return.

Question 17

Suppose you purchase one share of the stock of Volatile Engineering Corporation at the beginning of year 1 for $36.At the end of year 1,you receive a $2 dividend,and buy one more share for $30.At the end of year 2,you receive total dividends of $4 (i.e. ,$2 for each share),and sell the shares for $36.45 each.The time-weighted return on your investment is _________.

Accepted Answer

To calculate the time-weighted return, we need to consider the returns over each time period separately and then combine them.

For the first time period (from the beginning of year 1 to the end of year 1), we received a $2 dividend on one share, and we bought one more share for $30. Therefore, our investment at the end of year 1 was $36 (the value of the first share) plus $30 (the cost of the second share) minus $2 (the dividend received) = $64.

For the second time period (from the end of year 1 to the end of year 2), we received a $2 dividend on each share, so we received a total of $4. At the end of year 2, we sold both shares for $36.45 each, so we received a total of $72.90.

Now, we can calculate the time-weighted return as follows:

(Ending value of investment / Beginning value of investment)^(1/number of years) - 1

For this investment, there were two time periods that were each one year long. Therefore:

Ending value of investment = $72.90 
Beginning value of investment = $64 
Number of years = 2

Time-weighted return = ($72.90 / $64)^(1/2) - 1 = 0.0853, or 8.53%

Therefore, the answer is C) 8.53%.

Question 18

To determine the optimal risky portfolio in the Treynor-Black Model,macroeconomic forecasts are used for the _________ and composite forecasts are used for the _________.

Accepted Answer

The answer of To determine the optimal risky portfolio in...

Question 19

The difference between the arithmetic average return and the geometric average return is __________ for stocks with a high variance of returns,compared to stocks with a low variance of returns.

Accepted Answer

The difference between the arithmetic average return and the geometric average return is higher for stocks with a high variance of returns because the geometric average accounts for compounding and is more affected by volatility.

Question 20

The total excess return on the Highwater Marx Bros.'s managed portfolio was _________.

Accepted Answer

The total excess return can be calculated by subtracting the portfolio's benchmark return from the portfolio's actual return. From the table given, the portfolio return is 6.75%, and the benchmark return is 7.75%. Therefore, the excess return is -1.00%, option B.

Quiz 20: Taxes, Inflation, and Investment Strategy