A bank buys 150 shares of a company on 1 January 2012 at a price of $156.30 per

Question

A bank buys 150 shares of a company on 1 January 2012 at a price of $156.30 per share. A dividend of $10 per share is paid on 1 January 2013. Assume that this dividend is not reinvested. Also on 1 January 2013, the bank sells 100 shares at a price of $165 per share. On 1 January 2014, the bank collects a dividend of $15 per share (on 50 shares) and sells its remaining 50 shares at $170 per share. A. Write the formula to calculate the money-weighted rate of return on the bank’s portfolio. B. Calculate the time-weighted rate of return on bank’s portfolio.

Explanation / Answer

Answer :- Money-Weighted Rate of Return

Investment (buy) = 150 * 156.30

= 23445

Use Hit and Trail Method

Assume rate = 10%

Investment = Cash Inflow * PVIF at ( r , n )

23445 = [(16500+1500) * PVIF at (10%, 1year)] + [(8500+750) * PVIF at (10%, 2 year)]

23445 = 24002.5

(Inflow not equal to outflow)

Assume rate = 14%

Investment = Cash Inflow * PVIF at ( r , n )

23445 = [(16500+1500) * PVIF at (14%, 1year)] + [(8500+750) * PVIF at (14%, 2 year)]

23445 = 22899.25

(Inflow not equal to outflow)

Money-Weighted Rate of Return = 10% + [(24002.5 - 23445) / (24002.5 - 22899.25)] * (14% - 10%)

= 10% + [557.5 / 1103.25] * 4

= 12.02%

Time-Weighted Rate of Return

Holding period return = (Ending value - Begning Value + Dividend) / Begning value

Holding period return in 1 year = (Ending value - Begning Value + Dividend) / Begning value

= (165 - 153.6 + 10) / 156.3

= .1196 = 11.96%

Holding period return in 2 year = (Ending value - Begning Value + Dividend) / Begning value

= (170 - 165 + 15) / 165

= .1212 = 12.12%

Time Weighted Rate of Return = [{(1 + .1196) * (1 + .1212)} - 1] 1/2 [ 2 = no. of years]

= [{(1.1196) * (1.1212)} - 1] 1/2

= 12.765%

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