Question

Kevin Investor purchased shares of Torchwood security on the open of January 2 at $50.83 per share. H e earned a dividend of $1.20 in February. Kevin kept his dividend in cash. He did not reinvest it. Torchwood security closed at each month end as following: Jan=$51.20, Feb= $48.53, Mar=$49.87. Therefore, the total time-weighted rate of return for the calendar quarter is?

Answer 1

The time-weighted return also called geometric return that is calculated by multiplying various holding period returns

TWR = [(1+HPR1) * (1+HPR1) * (1+HPR1)] - 1 = [(1+0.03089) * (1+(-0.0521)) * (1+0.0276)] - 1 = [1.03089*0.9479*1.0276] - 1 = 1.00415 - 1 = 0.00415 =0.415 %

WHERE,

TWR - Time-weighted return

HPR - Holding period return

Holding period return = (End value - initial value + cash flow) / initial value  

HPR for period 1 = ($51.20 -$50.83 + $1.2 ) / $50.83 = $1.57 / $50.83 = 0.03089 = 3.0887%

HPR for period 1 = ($48.53 -$51.20 + $0 ) / $51.20 = -$2.67 / $51.20 = -0.0521 =- 5.21%

HPR for period 1 = ($49.87 -$48.53 + $0) / $48.53 = $1.34 / $48.53 = 0.0276 = 2.76%

Hence total time-weighted rate of return for the calendar quarter is 0.415%

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