Introduction

The Karnosky-Singer (KS) approach to currency attribution is rather different to the classical Brinson approach, and we highlight the differences in this overview document.

Firstly, KS attribution requires that asset allocation and stock selection are calculated using the local return premium, which is simply the local return of each asset, minus the interest rate applicable to that asset. Just as the real yield of a security is its market yield, minus inflation, the return premium is its local market return, minus the investment return; this gives a truer picture of where the returns come from.

Secondly, all FX returns are aggregated into a single ‘currency allocation’ term. This includes FX return generated by the physical positions, plus FX return generated by the hedge (if present). This not active FX return in the usual sense; it is instead an asset allocation return.

It’s not obvious that the sum of these terms should add up to the active base return for the portfolio, plus hedge, against the benchmark; that it does is shown in Appendix A [to be added].

For convenience, FIA still shows return due to asset allocation, stock selection and FX when Karnosky-Singer attribution is in use. However, the user should remain aware that the basis of the calculation of these quantities is quite different to the usual approach.

Worked example

Consider the following portfolio and benchmark, where the base currency is AUD:

Portfolio

Benchmark

The base currency return of the portfolio is 8.305%, and that of the benchmark 8.1%, so the overall outperformance is 0.205%.

Now, suppose that we add a currency hedge to the portfolio:

Note that the sum of all weights is zero (the hedge exists to change the FX tilt of the portfolio, not to change its asset allocation) and that the local returns are set to zero, so that  all hedge returns are treated as FX movements. Using FIA on this data generates the following results:

which is consistent with K&S’s original paper. We refer to this approach, which uses raw base and local returns for each security, as naïve currency attribution – not because it is wrong, but because it omits some information used in the Karnosky-Singer framework.

Karnosjy and Singer make a detailed case for including cash return in this type of analysis. The reader is referred to their original paper, or to Laker’s account, for more information.

To use the KS methodology in FIA, run the following four steps:

1. Set the local and base returns in the portfolio and benchmark files to the local return premium (local return minus cash rate).[2]
2. Set the base returns for hedges to the fx return plus cash rate. Set local returns to zero.
3. Weights of physical securities are unchanged.
4. Weights of hedge securities are set to (hedge weight – benchmark weight). This is equivalent to adding the active portfolio weight to the hedge weight.

This data is available in the KS2 dataset.

Results are

which is also consistent with K&S’s original paper. Note that the stock selection return is unchanged.

Running KS attribution in FIA

The current release of FIA requires some work by the user to implement KS attribution. When the KS switch is set to ‘on’:

• For physical assets, local and base returns must be replaced by local return premia (local return minus cash rate).
• For hedge assets, base returns are placed by ED rates (FX return plus cash rate).

[1] These numbers are taken from Karnosky and Singer’s original 1994 monograph [1], and Laker’s paper [2]

[2] By design, this ensures that no FX returns are generated by AA and SS.