Question

A Swedish investor having a portfolio of Swedish and American stocks. Their respective benchmarks are the OMX index and the S&P index. There have been no movements during the year (cash flows, sales, or purchases, dividends paid). Valuation and performance analysis is done in Swedish krona (SKr). Here are the valuations at the start and the end of the year:

	January 1	December 31
Swedish Stocks	SKr 800,000	SKr 900,000
U.S. Stocks	SKr 800,000	SKr 1,000,000
Total	SKr 1,600,000	SKr 1,900,000
Exchange Rate	7 SKr per $	8 SKr per $
OMX Index	110	130
S&P Index	110	135

1. What is the total return on the portfolio?   
2. Decompose this return into capital gain, yield, and currency contribution.

  

3. What is the contribution of security selection?

Answer 1

a)

Total value of portfolio on January 1st

= Skr800,000 + Skr800,000 = Skr1,600,000

Total value of portfolio on December 31st

= Skr900,000 + Skr1,000,000 = Skr1,900,000

Return on portfolio = (Skr1,900,000 - Skr1,600,000)/Skr1,600,000 = 18.75%

Note : The portfolio value of US stocks are also mentioned in Skr, so not used the exchange rate to translate. If it was given in $ then we will convert it using Exchange rate)

b)

Capital gain on sweedish stocks = (Skr900,000 - Skr800,000)/Skr800,000 = 12.5%

Converting the the US stocks portfolio value into $

Value on January 1 = Skr800,000/7 = $114,285.714

Value on December 31 = Skr1,000,000/8 = $125,000

Capital gain on US portfolio = ($125,000-$114,285.714)/$114,285.714 = 9.375%

Total gain on US portfolio is (Skr1,000,000-Ske800,000)/Skr800,000 = 25%

So currency gain is = Total gain on US portfolio - Capital gain on US portfolio = 25% - 9.375% = 15.625%

There is no dividend details given in the question, so no Yield Contribution

Capital gain contribution =

Currency contribution = (0 x Skr800,000/Skr1,600,000) + (15.625% x Skr800,000/Skr1,600,000)

= 7.8125%

Capital gain Contribution = (12.5% x Skr800,000/Skr1,600,000) + (9.375% x Skr800,000/Skr1,600,000)

= 10.9375%

Check : Total return = Capital gain contribution + Currency Contribution + Yield Contribution

18.75% = 10.9375% + 7.8125%

18.75% = 18.75%

c)

Contribution on security selection

Return on OMX index = (130-110)/110 = 18.18%

Return on S&P index = (135-110)/110 = 22.73%

Average rate of return on portfolio at 50% weights each = (18.18 + 22.73)/2 = 20.45%

Capital gain Contribution = 10.9375%

So contribution of security selection is -9.517% (negative return) (10.9375%-20.45%)

(We will not consider the currency contribution in measuring the contribution of portfolio selection)