Q3. 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%.

Q4. 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)   51.7%.

C)   51.4%.

答案和详解如下：

Q3. 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%.

Correct answer is A)

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%.

Q4. 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)   51.7%.

C)   51.4%.

Correct answer is C)         

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%.

answer

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