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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.20.52%
B.9.86%
C.14.48
Answer:A
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%.
