The following figure shows two key data inputs. These include the local return fund, which displays the return of the portfolio's asset segment in the local currency, and the local index return, which displays the benchmark's asset segment in the local currency.

The local cash return displays the local risk-free cash rate in each currency. In this example, the local cash return you can earn on a USD investment, such as a U.S. Treasury bill, is 7.5%.
The exchange rate return displays the currency appreciation and depreciation rates. Over the period, the EUR investment got stronger. And the JPY and GBP investments got weaker relative to the U.S. dollar.

 The Karnosky-Singer attribution process then calculates intermediate returns, which are used to calculate the market selection, security selection, and currency selection effects. The following figure shows four key intermediate returns. These include the local market return premiums for the portfolio and the benchmark, which is the difference between the local return and the local cash return, and the cash return for the portfolio and the benchmark, which is the sum of the local cash return and the exchange rate return.

In the previous figure, the local cash return for the EUR investment is 5% and the exchange rate return is 1%. So, the manager earned 6% in base currency terms. In the following figure, the cash return for the portfolio and the benchmark is also 6%.

Since the manager is not doing any hedging, the hedge returns for the portfolio and the benchmark are the same as the unhedged base currency returns. The total hedge return fund is 8.35% and the total hedge return index is 8.10%. The hedge return difference displays the difference between those returns ─ the excess return. This analysis shows that the manager outperformed the overall benchmark by 0.255% in base currency.

To analyze or measure the results of the manager's actions, the Karnosky-Singer attribution process decomposes the asset returns into three effects. These include the currency selection, market selection, and security selection effects. Once decomposed, the effects can be aggregated to the total level and attributed separately.

In the following figure, the total attributed value is 0.255%. This is the excess return or the value added by active portfolio management. It is the sum of the currency selection, market selection, and security selection effects.
The market selection effect also measures the impact of decisions to overweight or underweight particular asset segments relative to the benchmark. In the following figure, a positive market selection effect resulted from overweighting countries that produced greater returns than the benchmark average. However, a negative currency selection effect resulted from the currency exposure that came along with those weights.
The Karnosky-Singer attribution provides a true separation between the effects of the market decisions and currency decisions.

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Example 2: Synthetic Hedging

If you have a separate currency manager creating an overlay to adjust currency exposure, you can simulate the resulting currency exposure using one of three synthetic hedging options. You cannot have hedging instruments within your portfolio if you choose one of the synthetic currency hedging options. However, you can have hedging instruments within your portfolio if you are not hedging synthetically.

Hedge to 100% Portfolio to Base Currency Exposure

In the following figure, the manager simulated the hedging of all foreign currency exposures to the portfolio's base currency. Using the Hedge to 100% Portfolio to Base Currency Exposure option, he reduced the EUR currency exposure from 60% to 0%, the GBP currency exposure from 10% to 0%, and the JPY currency exposure from 10% to 0%. And he held all of his currency weights in U.S. dollars.

Hedge to 100% Portfolio to Base Currency Exposure - Weights
As we can see in the following figure, the market selection effects and the security selection effects remain unchanged as a result of this strategy. This is to be expected since the manager only shifted the currency exposure. Only the currency selection effect has changed. The negative currency selection effect that we saw in figure, Karnosky –Singer Effects (-0.71%) has changed to a positive currency selection effect (+.062%) in the following figure. And that currency selection effect was added to the market selection effect and security selection effect to calculate the total attributed value, which is equal to the difference between the hedged return of the portfolio and the return of the benchmark.

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Hedge to Benchmark Neutral Currency Exposure

In the following figure, the manager simulated the hedging of all currency exposures to be neutral to the benchmark's currency exposure. Using the Hedge to Benchmark Neutral Currency Exposure option, the manager reduced EUR currency exposure from 60% to 25%, increased GBP currency exposure from 10% to 25%, increased JPY currency exposure from 10% to 25%, and increased USD currency exposure from 20% to 25%. The currency weights of the portfolio are now equal to the weights of the benchmark.

As we can see in the following figure, the market selection effects and the security selection effects remain unchanged as a result of this strategy. Only the currency selection effect has changed. When the portfolio's currency exposure is the same as the benchmark's currency exposure, there is no active currency selection effect.

Hedge Using Weights Specified by Policy Benchmark

In the following figure, the manager simulated currency exposure by hedging all currency exposures independently and explicitly for each of the currencies. The weight the manager wanted to hedge for each currency was specified using the Hedge Policy Benchmark.

Using the Hedge Weights Specified by Policy Benchmark option, she reduced most of the EUR currency exposure from 60% to 10%, increased GBP currency exposure from 10% to 55%, increased JPY currency exposure from 10% to 25%, and decreased USD exposure from 20% to 10%.

As we can see in the following figure, the market selection effects and the security selection effects remain unchanged as a result of this strategy. Only the currency selection has changed. The currency selection effect measures the impact of overweighting or underweighting currency exposures in the portfolio relative to the benchmark. This is a highly successful currency strategy. The analysis shows that the manager outperformed the overall benchmark by 1.41%.