clearlycanadian

A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return?

A) 27.5%.

B) 22.0%.

C) 24.0%.

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(75 − 60 + 1.50) / 60 = 27.5%.

clearlycanadian

If an investor bought a stock for $32 and sold it one year later for $37.50 after receiving $2 in dividends, what was the holding period return on this investment?

A) 17.19%.

B) 23.44%.

C) 6.25%.

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HPR = [D + End Price − Beg Price] / Beg Price
HPR = [2 + 37.50 − 32] / 32 = 0.2344.

clearlycanadian

A bond was purchased exactly one year ago for $910 and was sold today for $1,020. During the year, the bond made two semi-annual coupon payments of $30. What is the holding period return?

A) 12.1%.

B) 18.7%.

C) 6.0%.

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HPY = (1,020 + 30 + 30 – 910) / 910 = 0.1868 or 18.7%.

clearlycanadian

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 time-weighted rate of return?

A) 0.06%.

B) 6.35%.

C) 11.24%.

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The holding period return in year one is ($89.00 − $100.00 + $1.00) / $100.00 = -10.00%.
The holding period return in year two is ($98.00 − $89.00 + $1.00) / $89 = 11.24%.
The time-weighted return is [{1 + (-0.1000)}{1 + 0.1124}]1/2 – 1 = 0.06%.

clearlycanadian

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) 6.35%.

B) 5.29%.

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%.

clearlycanadian

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) 9.86%.

B) 20.52%.

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%.

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%.