Holding Period Return Question

CFA Level I Quant
#1

Hi,

The answer below shows the return for the first holding period as 60% which assumes P1 (ending value) as $75. Shouldn’t P1 = $100 since “she sells both shares for $100 each.”?

Thanks for in advance for helping me understand this.

-j

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)

51.7%.

B)

23.2%.

C)

51.4%.

D)

21.4%.

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%.

#2

You should see it like this:

0 (today) --> 50 purchase

1 --> 75 purchase + 5

2 --> 100 * 2 = 200 + 15

HPR1= 80/50 = 1.6

HPR2 = 215/(75*2)= 1.43

See this problem:

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?

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%

they eliminate the amounts of shares bought… they make it like if you only had one share, you can make it like I did it or like these both problems taking only one share into account in the moment of selling, it is the same for return´s purpose

#3

thanks