94 RETURN MEASUREMENT
was less than the short-term gain. Therefore, the net amount is taxed at the short-term tax rate. If the amount is negative, the long-term loss was greater than the short-term gain. The net negative amount is taxed at the long-term tax rate to determine the tax benefit.
There are several other considerations for special situations when calcu- lating returns according to the SEC rule, but this example shows how after-tax returns are calculated for most situations.
Adjusting Returns for Impact of Fees, Taxes, and Currency 95
The market values of a fund managed in U.S. dollars over five days are in Column B. In Column H we have converted them to Canadian dollars using the exchange rates in Column E. The exchange rates here are quoted such that if the exchange rate increases, a foreign investor with a U.S.-dollar-based investment will experience a gain measured in his home currency. For example, the exchange rate of 0.62 on Day 2 indicates that 1 U.S. dollar is worth 0.62 Canadian dollars. So we multi- ply the market value of the holding in U.S. dollars by the exchange rate in order to determine the value in Canadian dollars. Exchange rates are not always quoted in this way; if the exchange rates were instead quoted as Canadian dollars per U.S. dollar then we would divide by the exchange rate to determine the value. Once we have converted the val- ues we calculate the fund’s return in Canadian dollars in the same way as we do the return in U.S. dollars. On Day 2 we record a loss of 3.556%. This loss is due to a combination of the decrease in market value as well as the decrease in the U.S./Canada exchange rate. On Day 3 the Canadian dollar is worth 1.587% less than it was on the day before. We can isolate the currency loss by calculating a currency return, equal to the change in exchange rates divided by the beginning exchange rate.
(6.17)
Another way to calculate the return converted to Canadian dollars is to instead take the return in U.S. dollars and multiply it by the cur- rency return. This return will approximate the return calculated by the first method in all situations except if there were cash flows into the fund at different exchange rates during the day (Just as if we had cash flows into the fund at different values in base currency during the day).
(6.18) In Column K we calculate the currency return using this method.
One advantage of using this method is that we don’t actually need to convert each day’s returns in order to convert a multiple period return to a different base currency. In Cell K10 we convert the 5-day return in U.S. dollars, which was 0.00%, to Canadian dollars by multiplying by the 5-day exchange rate return, 3.226%. This is a useful shortcut when we convert returns over long periods of time.
Currency return End exchange rate Begin exchange rate– Begin exchange rate
---
=
×100
Currency converted return 1+Fund return
( )×(1+Currency return)–1
=
CHAPTER 7
97
Measuring Relative Return
fter calculating the return on our fund, or a fund we are managing on behalf of someone else, the natural next step is to think about whether or not we are happy with the result. The periodic returns we calculate quantify how our investments have performed. To determine whether or not we are satisfied with our performance given the general market condi- tions, we need to have a basis of comparison. Performance comparisons are individualized according to investor or fund-specific objectives and constraints. Return requirements, tolerance for risk, income, and liquidity requirements guide the investment policy for the portfolio. The invest- ment policy guides the allocation to asset classes, managers, and strategies.
Given a basis of comparison, we might need to temper our spending and capital accumulation projections, adjust our investment strategy, change our investment manager, or make other changes. There are three possible reference points for comparison.
■ A target or projected return for the portfolio.
■ The return earned by funds with a similar purpose and strategy.
■ The market return for the asset class, as represented by a market index or benchmark customized for the strategy.
The first option is straightforward. We compare the results to the target return. But given that markets fluctuate, if we had an absolute long-term average goal in mind, we would not expect to earn that target return in any one period. For example, if the market is down 20% in a period and our fund is down 15%, while none of us has a long-term investment objective of losing money, we would be happy with our per- formance on a relative basis. So the peer group and benchmark compar- ison alternatives are of value even for funds with specific return
A
98 RETURN MEASUREMENT
objectives. In this chapter we look at the process for comparing our returns to those earned by other funds or peer groups.
The second option seeks to compare our performance to that earned by similar funds. Here we demonstrate the construction of peer group universes and the calculation of peer group average returns, which are commonly used as a basis for comparison. Finally, market indices and other benchmarks are commonly used to measure the success of an investment strategy. The selection of the manager’s benchmark is an important consideration. The benchmark serves to ensure that the inter- ests of the fund and manager are aligned. We also discuss at a summary level the methodology behind the third option—the creation and calcu- lation of returns for market indices and other comparison benchmarks.
This chapter covers the techniques for making performance compar- isons. By comparing the returns earned to the market or peer returns for the period, we can find out if our absolute performance was reasonable.
For measuring the performance of the manager, however, it is the rela- tiveperformance that is of interest. The chapter closes with a discussion of the methodology for determining the relative value added by the manager over time.