Reading 6: Discounted Cash Flow Applications-LOS d 习题精选 2011, interpret, measures, between, return

1215

Session 2: Quantitative Methods: Basic Concepts
Reading 6: Discounted Cash Flow Applications

LOS d: Calculate, interpret, and distinguish between the money-weighted and time-weighted rates of return of a portfolio, and appraise the performance of portfolios based on these measures.

 

 

On January 1, Jonathan Wood invests $50,000. At the end of March, his investment is worth $51,000. On April 1, Wood deposits $10,000 into his account, and by the end of June, his account is worth $60,000. Wood withdraws $30,000 on July 1 and makes no additional deposits or withdrawals the rest of the year. By the end of the year, his account is worth $33,000. The time-weighted return for the year is closest to:

A) 7.0%.

B) 5.5%.

C) 10.4%.

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January – March return = 51,000 / 50,000 ? 1 = 2.00%
April – June return = 60,000 / (51,000 + 10,000) ? 1 = –1.64%
July – December return = 33,000 / (60,000 ? 30,000) ? 1 = 10.00%
Time-weighted return = [(1 + 0.02)(1 ? 0.0164)(1 + 0.10)] ? 1 = 0.1036 or 10.36%

1215

Which of the following is most accurate with respect to the relationship of the money-weighted return to the time-weighted return? If funds are contributed to a portfolio just prior to a period of favorable performance, the:

A) money-weighted rate of return will tend to be elevated.

B) time-weighted rate of return will tend to be elevated.

C) money-weighted rate of return will tend to be depressed.

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The time-weighted returns are what they are and will not be affected by cash inflows or outflows. The money-weighted return is susceptible to distortions resulting from cash inflows and outflows. The money-weighted return will be biased upward if the funds are invested just prior to a period of favorable performance and will be biased downward if funds are invested just prior to a period of relatively unfavorable performance. The opposite will be true for cash outflows.

1215

The money-weighted return also is known as the:

A) return on invested capital.

B) internal rate of return (IRR) of a portfolio.

C) measure of the compound rate of growth of $1 over a stated measurement period.

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It is the IRR of a portfolio, taking into account all of the cash inflows and outflows.

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Which of the following statements regarding the money-weighted and time-weighted rates of return is least accurate?

A) The money-weighted rate of return removes the effects of the timing of additions and withdrawals to a portfolio.

B) The time-weighted rate of return reflects the compound rate of growth of one unit of currency over a stated measurement period.

C) The time-weighted rate of return is the standard in the investment management industry.

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The money-weighted return is actually highly sensitive to the timing and amount of withdrawals and additions to a portfolio. The time-weighted return removes the effects of timing and amount of withdrawals to a portfolio and reflects the compound rate of growth of $1 over a stated measurement period. Because the time-weighted rate of return removes the effects of timing, it is the standard in the investment management industry.

1215

An analyst managed a portfolio for many years and then liquidated it. Computing the internal rate of return of the inflows and outflows of a portfolio would give the:

A) time-weighted return.

B) net present value.

C) money-weighted return.

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The money-weighted return is the internal rate of return on a portfolio that equates the present value of inflows and outflows over a period of time.

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Time-weighted returns are used by the investment management industry because they:

A) result in higher returns versus the money-weighted return calculation.

B) are not affected by the timing of cash flows.

C) take all cash inflows and outflows into account using the internal rate of return.

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Time-weighted returns are not affected by the timing of cash flows. Money-weighted returns, by contrast, will be higher when funds are added at a favorable investment period or will be lower when funds are added during an unfavorable period. Thus, time-weighted returns offer a better performance measure because they are not affected by the timing of flows into and out of the account.

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Why is the time-weighted rate of return the preferred method of performance measurement?

A) Time weighted allows for inter-period measurement and therefore is more flexible in determining exactly how a portfolio performed during a specific interval of time.

B) Time-weighted returns are not influenced by the timing of cash flows.

C) There is no preference for time-weighted versus money-weighted.

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Money-weighted returns are sensitive to the timing or recognition of cash flows while time-weighted rates of return are not.

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Which of the following statements about money-weighted and time-weighted returns is least accurate?

A) The money-weighted return applies the concept of internal rate of return to investment portfolios.

B) If the investment period is greater than one year, an analyst must use the geometric mean to calculate the annual time-weighted return.

C) If a client adds funds to an investment prior to an unfavorable market, the time-weighted return will be depressed.

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The time-weighted method is not affected by the timing of cash flows. The other statements are true.

1215

An investor buys four shares of stock for $50 per share. At the end of year one she sells two shares for $50 per share. At the end of year two she sells the two remaining shares for $80 each. The stock paid no dividend at the end of year one and a dividend of $5.00 per share at the end of year two. What is the difference between the time-weighted rate of return and the money-weighted rate of return?

A) 20.52%.

B) 9.86%.

C) 14.48%.

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T = 0: Purchase of four shares = -$200.00

T = 1: Dividend from four shares = +$0.00

Sale of two shares = +$100.00

T = 2: Dividend from two shares = +$10.00

Proceeds from selling shares = +$160.00

The money-weighted return is the rate that solves the equation:

$200.00 = $100.00 / (1 + r) + $170.00 / (1 + r)².

Cfo = -200, CF1 = 100, Cf2 = 170, CPT → IRR = 20.52%.

The holding period return in year one is ($50.00 ? $50.00 + $0.00) / $50.00 = 0.00%.

The holding period return in year two is ($80.00 ? $50.00 + $5.00) / $50 = 70.00%.

The time-weighted return is [(1 + 0.00)(1 + 0.70)]^1/2 ? 1 = 30.38%.

The difference between the two is 30.38% ? 20.52% = 9.86%.

1215

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s money-weighted rate of return?

A) 5.29%.

B) 6.35%.

C) 0.06%.

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T = 0: Purchase of first share = -$100.00

T = 1: Dividend from first share = +$1.00

Purchase of 3 more shares = -$267.00

T = 2: Dividend from four shares = +4.00

Proceeds from selling shares = +$392.00

The money-weighted return is the rate that solves the equation:

$100.00 = -$266.00 / (1 + r) + 396.00 / (1 + r)².

CFO = -100; CF1 = -266; CF2 = 396; CPT → IRR = 6.35%.