[1] Quantitative Methods _ Curriculum

The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for:

• maturity.
• liquidity.
• expected inflation.

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?

• Inflation
• Maturity
• Liquidity

• 14.9 percent.
• 15.6 percent.
• 19.5 percent.

A portfolio manager invests EUR 5,000 annually in a security for four years at the following prices:

• harmonic mean of EUR 76.48.
• geometric mean of EUR 77.26.
• arithmetic average of EUR 78.00.

Which of the following statements regarding arithmetic and geometric means is correct?

• The geometric mean will exceed the arithmetic mean for a series with non-zero variance.

• The geometric mean measures an investment’s compound rate of growth over multiple periods.

• The arithmetic mean measures an investment’s terminal value over multiple periods.

A fund receives investments at the beginning of each year and generates returns for three years as follows:

• Geometric mean return

• Time-weighted rate of return

• Money-weighted rate of return

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:

• less than the time-weighted rate of return.

• the same as the time-weighted rate of return.

• greater than the time-weighted rate of return.

An investor is evaluating the returns of three recently formed ETFs. Selected return information on the ETFs is presented in Exhibit 20:

• ETF 1

• ETF 2

• ETF 3

The price of a stock at t = 0 is USD 208.25 and at t = 1 is USD 186.75. The continuously compounded rate of return, r1,T for the stock from t = 0 to t = 1 is closest to:

• –10.90 percent.

• –10.32 percent.

• 11.51 percent.

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:

• 11.0 percent.

• 11.2 percent.

• 13.2 percent