You are a Swedish investor owning 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 purchase). Dividends of SKr 20,000 have been paid on Swedish stocks. Valuation and performance analysis is done in Swedish krona (SKr). Here are the valuations at the start and the end of the year:
$$\begin{array} { l r r }
& \text { January 1 } & \text { December 31 } \
\hline \text { Swedish Stacks } & \text { SKr 600,000 } & \text { SKr 660,000 } \
\text { U.S. Stacks } & \$ 100,000 & \$ 140,000 \
\text { Cash } & 0 & \text { SKr 20,000 } \
\text { Exchange Rate } & 6 \text { SKr/\$ } & 5.5 \mathrm { SKr } / \$ \
\text { OMX Index } & 100 & 120 \
\text { S\&p Index } & 100 & 125
\end{array}$$ a. What is the total value of the portfolio in SKr on January 1 and on December 31?
b. What is the total return on the portfolio?
c. Decompose this return into capital gain, yield, and currency contribution.
d. What is the contribution of security selection?

Question

You are a Swedish investor owning 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 purchase). Dividends of SKr 20,000 have been paid on Swedish stocks. Valuation and performance analysis is done in Swedish krona (SKr). Here are the valuations at the start and the end of the year:
 $$\begin{array} { l r r } 
& \text { January 1 } & \text { December 31 } \
\hline \text { Swedish Stacks } & \text { SKr 600,000 } & \text { SKr 660,000 } \
\text { U.S. Stacks } & \$ 100,000 & \$ 140,000 \
\text { Cash } & 0 & \text { SKr 20,000 } \
\text { Exchange Rate } & 6 \text { SKr/\$ } & 5.5 \mathrm { SKr } / \$ \
\text { OMX Index } & 100 & 120 \
\text { S\&p Index } & 100 & 125
\end{array}$$ a. What is the total value of the portfolio in SKr on January 1 and on December 31?
b. What is the total return on the portfolio?
c. Decompose this return into capital gain, yield, and currency contribution.
d. What is the contribution of security selection?

Quizplus · Accepted Answer

The Answer is a. The total SKr value of the portfolios on January 1 is:
SKr 600,000+ $100,000 * 6 SKr/$=SKr (600,000 + 600,000) = SKr 1,200,000.
The total SKr value of the portfolios on December 31 is:
SKr 660,000 + $140,000 *5.5 SKr/$ + SKr 20,000 =SKr (660,000 + 770,000 + 20,000)
= SKr 1,450,000.
b. The total return on the portfolio, measured in SKr is equal to:

\frac { 1,450,000 } { 1,200,000 } - 1 = 0.2083 ext { or } 20.83 \%

c. The capital gains amounts to:

\bullet

660,000 - 600,000 = SKr 60,000 on the Swedish stocks or 10%,

\bullet

$140,000 - $100,000 = $40,000 on the U.S. stocks or 40%.
If we use the SKr 6/$ exchange rate, this is (40,000)(6) = SKr 240,000. The total capital gain is then SKr 300,000 or 25%. Notice that this corresponds to a capital gain in local currency equal
to 0.5 * 10% + 0.5 * 40% =25%.
Also note that:

\bullet

The dollar return on U.S. stock is 40% = 40,000/100,000.

\bullet

The SKr return on U.S. stocks is 28.33% = (770,000 - 600,000)/600,000.
The yield comes from the dividends paid on Swedish stocks and can be calculated as follows:
Yield on Swedish stocks=SKr 20,000/SKr 600,000 = 3.33%.
Portfolio yield = Portfolio weights of Swedish stocks * yield of Swedish stocks
= 0.5*3.33% = 1.67%.
The currency contribution can be calculated as follows:
Currency contribution of U.S. investments =SKr return on U.S. stocks - $ return on U.S. stocks
= 28.33% -40% = -11.67%.
Portfolio currency contribution = Portfolio weights of U.S. stocks * currency contribution
= 0.5* (-11.67%) = -5.84%.
The total return of the portfolio can be decomposed as follows:
Total return of the portfolio =Capital gain + Yield +Currency contribution
= 25% + 1.67% -5.84%= 20.83%.
d. If the same amounts had been invested respectively in the OMX index and in the S&P index, returns would have been the following:

\bullet

20% on the Swedish index.

\bullet

25% on the U.S. index.

\bullet

Portfolio-weighted market return in local currency = 0.5 *0.20 + 0.5 * 0.25 = 0.225 =22.5%.
We would have obtained 22.5% in local currency while our realized capital gain was 25%. Hence, security selection contributed positively for 2.5%. The Swedish portfolio only achieved a 10% capital gain, while the OMX index showed a 20% growth. However, the U.S. stock portfolio achieved a 40% capital gain (in dollars), while the S&P index showed a 25% appreciation.
Hence, the capital gain itself can be broken down into:

\begin{array} { l } \hline ext { Market } +& ext { Security selection } \\hline22.5 \%&2.5 \% \\hline \end{array}

You Are a Swedish Investor Owning a Portfolio of Swedish