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On January 1, 2016, Brian's stock portfolio is worth $100,000. On September 30, 2016, $5,000 is withdrawn from the portfolio, and immediately after this withdrawal the portfolio has a value of $105,000. Twelve months later, the value of the portfolio is $108,000, and Brian adds $3,000 worth of stock to his portfolio. On December 31, 2017, the portfolio is worth $100,000. What is the time-weighted rate of return for Brian's stock portfolio over the two year period

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Answer:

1.93%

Explanation:

The time weighted rate of return will be computed by combining the return at every time period demarcated by a withdrawal/addition.

Time 1: Jan 1, 2016 to Sep 30, 2016

start value = 100,000; end value = (105,000+5,000) = 110,000

Return = [tex]\frac{110,000}{100,000}=1.1[/tex]

Time 2: Sep 30, 2016 to Sep 30, 2017

start value = 105,000; end value = 108,000

Return = [tex]\frac{108,000}{105,000}=1.028571[/tex]

Time 3: Sep 30, 2017 to Dec 31, 2017

start value = (108,000 + 3,000) = 111,000; end value = 100,000

Return = [tex]\frac{100,000}{111,000}=0.900901[/tex].

Therefore, time weighted return

= (1.1 * 1.028571 * 0.900901) - 1

= 0.019305

= 1.93%.

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