clearlycanadian

An investor makes the following investments:

• She purchases a share of stock for $50.00.
• After one year, she purchases an additional share for $75.00.
• After one more year, she sells both shares for $100.00 each.
• There are no transaction costs or taxes.

During year one, the stock paid a $5.00 per share dividend. In year 2, the stock paid a $7.50 per share dividend. The investor’s required return is 35%. Her money-weighted return is closest to:

A) -7.5%.

B) 16.1%.

C) 48.9%.

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To determine the money weighted rate of return, use your calculator's cash flow and IRR functions. The cash flows are as follows: CF0: initial cash outflow for purchase = $50
CF1: dividend inflow of $5 - cash outflow for additional purchase of $75 = net cash outflow of -$70
CF2: dividend inflow (2 × $7.50 = $15) + cash inflow from sale (2 × $100 = $200) = net cash inflow of $215
Enter the cash flows and compute IRR:
CF0 = -50; CF1 = -70; CF2 = +215; CPT IRR = 48.8607

clearlycanadian

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.

clearlycanadian

An investor buys a share of stock for $200.00 at time t = 0. At time t = 1, the investor buys an additional share for $225.00. At time t = 2 the investor sells both shares for $235.00. During both years, the stock paid a per share dividend of $5.00. What are the approximate time-weighted and money-weighted returns respectively?

A) 10.8%; 9.4%.

B) 7.7%; 7.7%.

C) 9.0%; 15.0%.

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Time-weighted return = (225 + 5 − 200) / 200 = 15%; (470 + 10 − 450) / 450 = 6.67%; [(1.15)(1.0667)]1/2 − 1 = 10.8%
Money-weighted return: 200 + [225 / (1 + return)] = [5 / (1 + return)] + [480 / (1 + return)2]; money return = approximately 9.4%
Note that the easiest way to solve for the money-weighted return is to set up the equation and plug in the answer choices to find the discount rate that makes outflows equal to inflows.
Using the financial calculators to calculate the money-weighted return: (The following keystrokes assume that the financial memory registers are cleared of prior work.)
TI Business Analyst II Plus®

• Enter CF0: 200, +/-, Enter, down arrow
• Enter CF1: 220, +/-, Enter, down arrow, down arrow
• Enter CF2: 480, Enter, down arrow, down arrow,
• Compute IRR: IRR, CPT
• Result:  9.39

HP 12C®

• Enter CF0: 200, CHS, g, CF0
• Enter CF1: 220, CHS, g, CFj
• Enter CF2: 480, g, CFj
• Compute IRR: f, IRR
• Result:  9.39

clearlycanadian

Assume an investor makes the following investments:

• Today, she purchases a share of stock in Redwood Alternatives for $50.00.
• After one year, she purchases an additional share for $75.00.
• After one more year, she sells both shares for $100.00 each.

There are no transaction costs or taxes. The investor’s required return is 35.0%.
During year one, the stock paid a $5.00 per share dividend. In year two, the stock paid a $7.50 per share dividend.
The time-weighted return is:

A) 23.2%.

B) 51.4%.

C) 51.7%.

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To calculate the time-weighted return:
Step 1: Separate the time periods into holding periods and calculate the return over that period:

Holding period 1: P0 = $50.00
D1 = $5.00
P1 = $75.00 (from information on second stock purchase)
HPR1  = (75 − 50 + 5) / 50 = 0.60, or 60%
Holding period 2: P1 = $75.00
D2 = $7.50
P2 = $100.00
HPR2  = (100 − 75 + 7.50) / 75 = 0.433, or 43.3%.

Step 2: Use the geometric mean to calculate the return over both periods

Return = [(1 + HPR1) × (1 + HPR2)]1/2 − 1 = [(1.60) × (1.433)]1/2 − 1 = 0.5142, or 51.4%.

clearlycanadian

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) 10.4%.

C) 5.5%.

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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%

clearlycanadian

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

B) money-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.

clearlycanadian

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.

clearlycanadian

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

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

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

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

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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.

clearlycanadian

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) money-weighted return.

B) time-weighted return.

C) net present value.

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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.

clearlycanadian

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

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

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

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

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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.