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George Lennon buys 250 shares of ABB on 1 January 2016 at a price of $256.30...

George Lennon buys 250 shares of ABB on 1 January 2016 at a price of $256.30 per share. A dividend of $5 per share is paid on 1 January 2017. Assume that this dividend is not reinvested. Also on 1 January 2017, Lennon sells 90 shares at a price of $275 per share. On 1 January 2018, he collects a dividend of $7 per share (on 160 shares) and sells his remaining 160 shares at $299 per share. Calculate the time-weighted rate of return on Lennon's portfolio (write the answer in decimals, not %).

I calculated it and got 23.71% (0.2371) as a result and it was wrong.

Hope someone can help me out

Solutions

Expert Solution

Calculating Holding period return for 2016

Beginning value of portfolio = No of shares bought on 1 Jan 2016 x price per share on 1 Jan 2016 = 250 x 256.30 = 64075

Ending value of portfolio = Value of shares at end of 2016 + Dividends received = No of shares bought on 1 Jan 2016 x price per share on 1 Jan 2017 + No of shares bought on 1 Jan 2016 x dividend per share received on 1 Jan 2017 = 250 x 275 + 250 x 5 = 68750 + 1250 = 70000

Holding period return for 2016 = (Beginning value of portfolio - Ending value of portfolio) / Ending value of portfolio = (70000 - 64075) / 64075 = 5925 / 64025 = 0.092469 = 9.2469%

Calculating Holding period return for 2017

Since 90 shares have sold, thus beginning share balance as on 1 Jan 2017 = 160

Beginning value of portfolio = No of shares remaining on 1 Jan 2017 x price per share on 1 Jan 2017 = 160 x 275 = 44000

Ending value of portfolio = Value of shares at end of 2017 + Dividends received = No of shares remaining on 1 Jan 2017 x price per share on 1 Jan 2018 + No of shares remaining on 1 Jan 2017 x dividend per share received on 1 Jan 2018 = 160 x 299 + 160 x 7 = 47840 + 1120 = 48960

Holding period return for 2017 = (Beginning value of portfolio - Ending value of portfolio) / Ending value of portfolio = (48960 - 44000) / 44000 = 4960 / 44000 = 0.112727 = 11.2727%

Calculating time weighted return

Time weighted return = (1 + Holding period return for 2016)(1 + Holding period return for 2017) - 1 = (1 + 9.2469%)(1+11.2727%) - 1 = 1.092469 x 1.112727 - 1 = 1.2156 - 1 = 0.2156

Time weighted return = 0.2156

jeff jeffy answered 1 year ago
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