Question

Peter has an investment portfolio that paid him the rate of
returns of 9 %, 13%, -2%. 7% and 15% over the past five years. Required:
a) Calculate the arithmetic average return of the portfolio and
geometric average return of the portfolio?
b) If he bought 100 share A in that portfolio for $1500 five years ago,
the current market price of the share is $23 each and the share has
paid a dividend of $2/share each year since then, what is capital
gain and dividend yield of this share?

Answer 1

A) Average return = 9% + 13% - 2% + 7% +15% / 5

= 42% / 5

= 8.4%

Geometric return

= {(1+0.09) (1+0.13) (1-0.02) (1+0.07) (1+0.15)}^1/5 - 1

= {(1.09) (1.13) 0.98) (1.07) (1.15)}^0.2 - 1

= {1.48529}^0.2 - 1

= 1.0823 - 1

= 0.0823 or 8.23%

b) current value of share= current price × number of shares

= 23 × 100

= 2300

Capital gain = end value - beginning value / beginning value

= 2300 - 1500 / 1500

= 800 / 1500

= 53.33%

Dividend yield = dividend / old share price

= 2 / 15

= 13.33%

Note:

Old share price = total investment / no. Of share

= 1500 / 100

= 15