Quant - Rates & Return Flashcards
Correct. The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for:
A.maturity.
B.liquidity.
C.expected inflation.
C is correct. The nominal risk-free rate is approximated as the sum of the real risk-free interest rate and an inflation premium.
Which of the following risk premiums is most relevant in explaining the difference in yields between 30-year bonds issued by the US Treasury and 30-year bonds issued by a small, private US corporate issuer?
A.Inflation
B.Maturity
C.Liquidity
C is correct.
US Treasury bonds are highly liquid, whereas the bonds of small issuers trade infrequently and the interest rate includes a liquidity premium. This liquidity premium reflects the relatively high costs (including the impact on price) of selling a position. As the two bond issues have the same 30-year maturity, the observed difference in yields would not be solely explained by maturity. Further, the inflation premium embedded in the yield of both bonds is likely to be similar given they are both US-based bonds with the same maturity.
Consider the following annual return for Fund Y over the past five years:
The geometric mean return for Fund Y is closest to:
A.14.9 percent.
B.15.6 percent.
C.19.5 percent.
A is correct. The geometric mean return for Fund Y is calculated as follows:
RG
= (1 + 0.195)
× (1 − 0.019)
× (1 + 0.197)
× (1 + 0.350)
× (1 + 0.057)
− 1
= 14.9%.
A portfolio manager invests EUR5,000 annually in a security for four years at the following prices:
The average price is best represented as the:
A.harmonic mean of EUR76.48.
B.geometric mean of EUR77.26.
C.arithmetic average of EUR78.00.
A is correct.
The harmonic mean is appropriate for determining the average price per unit as it gives equal weight to each data point and reduces the potential influence of outliers. It is calculated as follows:
XH=
4/
[(1/62.00)
+ (1/76.00)
+ (1/84.00)
+ (1/90.00)]
= EUR76.48.
Which of the following statements regarding arithmetic and geometric means is correct?
A.The geometric mean will exceed the arithmetic mean for a series with non-zero variance.
B.The geometric mean measures an investment’s compound rate of growth over multiple periods.
C.The arithmetic mean measures an investment’s terminal value over multiple periods.
B is correct.
The geometric mean compounds the periodic returns of every period, giving the investor a more accurate measure of the terminal value of an investment.
A fund receives investments at the beginning of each year and generates returns for three years as follows:
Which return measure over the three-year period is negative?
A.Geometric mean return
B.Time-weighted rate of return
C.Money-weighted rate of return
C is correct. The money-weighted rate of return considers both the timing and amounts of investments into the fund. To calculate the money-weighted rate of return, tabulate the annual returns and investment amounts to determine the cash flows.
At the beginning of Year 1, a fund has USD10 million under management; it earns a return of 14 percent for the year. The fund attracts another net USD100 million at the start of Year 2 and earns a return of 8 percent for that year. The money-weighted rate of return of the fund is most likely to be:
A.less than the time-weighted rate of return.
B.the same as the time-weighted rate of return.
C.greater than the time-weighted rate of return.
A is correct.
How do you calculate the time-weighted rate of return?
Calculate the rate of return for each sub-period by subtracting the beginning balance of the period from the ending balance of the period and divide the result by the beginning balance of the period.
Create a new sub-period for each period that there is a change in cash flow, whether it’s a withdrawal or deposit. You’ll be left with multiple periods, each with a rate of return.
Add 1 to each rate of return, which simply makes negative returns easier to calculate.
Multiply the rate of return for each sub-period by each other. Subtract 1 from the result to achieve the TWR.
An investor is evaluating the returns of three recently formed ETFs.
Selected return information on the ETFs is presented in Exhibit 20:
Which ETF has the highest annualized rate of return?
A.ETF 1
B.ETF 2
C.ETF 3
B is correct. The annualized rate of return for
ETF 1 annualized return = (1.0425365/125) – 1 = 12.92%
ETF 2 annualized return = (1.019552/8) − 1 = 13.37%
ETF 3 annualized return = (1.171812/16) – 1 = 12.63%
Despite having the lowest value for the periodic rate, ETF 2 has the highest annualized rate of return because of the reinvestment rate assumption and the compounding of the periodic rate.
How do you calculate annualized return?
see image.
The price of a stock at
t = 0 is $208.25
and at
t = 1 is $186.75.
The continuously compounded rate of return, r1,T for the stock from t = 0 to t = 1 is closest to:
A.–10.90 percent.
B.–10.32 percent.
C.11.51 percent.
A is correct.
The continuously compounded return from t = 0 to t = 1 is r0,1 = ln(S1/S0) = ln(186.75/208.25) = –0.10897 = –10.90%.
How do you calculate continuously compounded return?
A USD25 million equity portfolio is financed 20 percent with debt at a cost of 6 percent annual cost.
If that equity portfolio generates a 10 percent annual total investment return, then the leveraged return is:
A.11.0 percent.
B.11.2 percent.
C.13.2 percent
A is correct.
An investment manager’s gross return is:
A.an after-tax nominal, risk-adjusted return.
B.the return earned by the manager prior to deduction of trading expenses.
C.an often used measure of an investment manager’s skill because it does not include expenses related to management or administration.
C is correct.
Gross returns are calculated on a pre-tax basis; trading expenses are accounted for in the computation of gross returns as they contribute directly to the returns earned by the manager.
A is incorrect because investment managers’ gross returns are pre-tax and not adjusted for risk.
B is incorrect because managers’ gross returns do reflect the deduction of trading expenses since they contribute directly to the return earned by the manager.
The strategy of using leverage to enhance investment returns:
A.amplifies gains but not losses.
B.doubles the net return if half of the invested capital is borrowed.
C.increases total investment return only if the return earned exceeds the borrowing cost.
C is correct.
The use of leverage can increase an investor’s return if the total investment return earned on the leveraged investment exceeds the borrowing cost on debt.
A is incorrect because leverage amplifies both gains and losses.
B is incorrect because, if half of the invested capital is borrowed, then the investor’s gross (not net) return would double.
At the beginning of the year, an investor holds EUR10,000 in a hedge fund.
The investor borrowed 25 percent of the purchase price, EUR2,500, at an annual interest rate of 6 percent and expects to pay a 30 percent tax on the return she earns from his investment.
At the end of the year, the hedge fund reported the information in Exhibit 22
The investor’s after-tax return on the hedge fund investment is closest to:
A.3.60 percent.
B.3.98 percent.
C.5.00 percent.
C is correct.
Over the past four years, a portfolio experienced returns of −8%, 4%, 17%, and −12%.
The geometric mean return of the portfolio over the four-year period is closest to:
A.
0.25%.
B.
−0.37%.
C.
0.99%.
B is correct.
The annualized return for an investor who has achieved a return of 5% over a six-week period is closest to:
A.
43.33%.
B.
52.63%.
C.
54.24%.
B is correct.
An investment in 10,000 common shares of a company for one year earned a 15.5% return.
The investor received a $2,500 dividend just prior to the sale of the shares at $24 per share.
The price that the investor paid for each share one year earlier was closest to:
A.
$20.80.
B.
$20.50.
C.
$21.00.
C is Correct.
The return measure that best allows one to compare asset returns earned over different length time periods is the:
A.
holding period return.
B.
annualized return.
C.
net portfolio return.
B is correct.
An investor purchases 100 shares of stock at $40 per share. The investor holds the shares for exactly one year and then sells all of them at $41.50 per share. On the date of sale, the investor receives dividends totaling $200. The holding period return (HPR) on the investment is closest to:
A.
8.75%.
B.
3.75%.
C.
8.43%.
A is correct.
Using a discount rate of 5%, compounded monthly, the present value (PV) of $5,000 to be received three years from today is closest to:
A.
$4,250.
B.
$4,319.
C.
$4,305.
C is Correct.
An investor deposits £2,000 into an account that pays 6% per annum compounded continuously. The value of the account at the end of four years is closest to:
A.
£2,525.
B.
£2,542.
C.
£2,854.
B is Correct.
Investor A and Investor B invest in a fund for two years:
Given the information in the table, which of the following is least likely to be an explanation for the difference between the two money-weighted rates of return?
A.
Investor A increased the investment in the fund at the end of year 1 whereas investor B did not make any additions or withdrawals.
B.
Investor B decreased the investment in the fund at the end of year 1 whereas investor A did not make any additions or withdrawals.
C.
The investors invested different amounts at inception and afterward did not make any additions or withdrawals.
C is Correct.
Assume the following:
The real risk-free rate of return is 3%.
The expected inflation premium is 5%.
The market-determined interest rate of a security is 12%.
The sum of the default risk premium, liquidity premium, and maturity premium for the security is closest to:
A.
10%.
B.
4%.
C.
8%.
B is correct.
If the price of a stock goes from $15.00 to $16.20 in one year, the continuously compounded rate of return is closest to:
A.
7.70%.
B.
8.33%.
C.
8.00%.
A is correct.
An investor purchases one share of stock for $85. Exactly one year later, the company pays a dividend of $2.00 per share. This is followed by two more annual dividends of $2.25 and $2.75 in successive years. Upon receiving the third dividend, the investor sells the share for $100. The money-weighted rate of return on this investment is closest to:
A.
7.97%.
B.
8.15%.
C.
8.63%.
B is Correct.
The minimum rate of return an investor must receive in order to accept an investment is best described as the:
A.
internal rate of return.
B.
required rate of return.
C.
expected return.
B is correct.
Consider the investment in the following table:
Assuming dividends are not reinvested, compared with the time-weighted return, the money-weighted return is:
A.
lower.
B.
the same.
C.
higher.
A is correct.
A portfolio provides the following returns over a five-year period.
The average compound rate of return of the portfolio across the five-year period is closest to:
A.
0.02%.
B.
1.00%.
C.
−9.31%.
A is correct.
The liquidity premium can best be described as compensation to investors for the:
A.
risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly.
B.
increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended.
C.
possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.
A is correct.
The 15-month holding period return for a security is 12%. Its annualized return is closest to:
A.
10.03%.
B.
9.60%.
C.
9.49%.
C is correct.
An analyst observes that the historic geometric nominal return for equities is 9%. Given a real return of 1% for riskless Treasury bills and annual inflation of 2%, the real rate of return and risk premium for equities are closest to:
A.
7.9% and 5.8%.
B.
6.9% and 7.9%.
C.
6.9% and 5.8%.
C is correct.
The quarterly returns on a portfolio are as follows:
The time-weighted rate of return of the portfolio is closest to:
A.
−5.0%.
B.
−1.3%.
C.0.0%.
A is Correct.
