Should currency be treated as a separate asset class? If currency hedging adds value to a portfolio, how should this be done

Lamper, D.

English

Mathematics in Industry Information Service Eprints Archive

Risk and Return Performance Attribution for Cross
Border Investment Portfolio
Should currency be treated as a separate asset class? If currency hedging adds value to a
portfolio, how should this be done?
where E[R] : Portfolio return,E[Rd] : Domestic asset return, E[Rf] : Foreign asset return,E[Rc]
Currency return, Wd : proportion in domestic assets,wf : proportion in foreign assets and
wd+wf=l.
The addition of foreign asset exposure affects both the return and risk of a portfolio. Consider
hedging foreign currency exposure using forward contracts: Domestic Assets; Foreign Assets;
Hedge.
Let S denote the spot foreign exchange rate and F denote forward exchange rate. Conversion
agreed to now, but transaction takes place at some point in the future
Forward contract return should be
S(T)F = R f
S(t) c
where f is the forward premium (or discount).
Combine forward contract with foreign asset,we have
where h is the fraction of asset exposure hedged.
Rearranging it we obtain
E[R] = wdE[Rd] + wf(E[Rf] + J) + H(E[Rc] - J)
with constraints Wd + wf = 1; 0 ~ H ~ wf
e.g. fully hedged (H = 0):
E[R] = wdE[Rd] + wf(E[Rf] + J)
Performance is often related to a benchmark portfolio. Risk and return should be measured
relative to benchmark. Managers generate excess returns by deviating from benchmark.
Excess return:
Performance of financial asset cannot be measured by the increase in capital alone, but also by
risk incurred during time required to achieve this return.
Measures of risk include: Standard deviation a, value at Risk (VaR), relative value at Risk
(ReVaR), tracking error and many more.
_R_iS_k_v_s_-_r_e_w_a_r_d vV
cr:
~ 0.13
E~
~ 0.125
"0
~8. 0.12
III
0.11
0.09 0.095 0.1 0.105 0.11 0.115 0.12
Standard deviation: 0
Domestic Foreign Currency
Expected Return E[Rd] = 11 % E[Rf] = 13 % E[Rcl = 2 %
Standard Deviation CJd= 10 % CJf = 12 % CJc= 8 %
Measure of risk based on a probability of loss, given a time horizon over which this loss can be
expected to occur
_V_a_lu_e_a_t _R_iS_k N
• Measure of risk based on a probability of loss, given a
time horizon over which this loss can be expected to
occur
\
\ peR < -VaR) == 1 - a
\
\,
• Developed for managing risk on derivative trading desks
over short time horizons, e.g. 1 or 2 days.
• Applicable to multi-asset class portfolios
Developed for managing risk on derivative trading desks over short time horizons, e.g. 1 or
2 days. Applicable to multi-asset class portfolios.
Calculating VaR over long time horizon, e.g. 3 months, requires estimation of mean m and
covariances S of assets within portfolio.
Incorporate hedge by treating as just another investment within portfolio.
Assume Normally distributed:
_V_a_R_v_s_R_e_t_u_r_n V'V
0.032
E.g 0.031
0:
"C 003
~
~O.029
ill
ReVaR vs. Excess Return V'V
.104,
-3o 0.(1)5 0.01 0015 002 0.025 003 O.lD5 004
ReVaR - 3 months
Limit VaR over short and long horizons.
Maximize expected return for a given risk exposure using optimization.
Include additional constraints, e.g. limit foreign exposure
Multipletime horizons
• limit VaR over short
and long horizons
• Maximise expected
return for a given risk
exposure using
optimisation
• Include additional
constraints, e.g.
o limit foreign
exposure
o ...
~o.ou
".•..•0012
'"~ 0.01
Increasing the complexity: l)Assume returns are Normally distributed, estimate parameters us-
ing historical data.2) Forecast parameters using market knowledge. 3)Incorporate more realistic
asset model, e.g. GARCR, stochastic volatility, mean-reverting exchange rates, unstable corre-
lations. 1) & 2) permit analytic expression for VaR. 3) requires simulation, but could improve
accuracy. Backtesting on historical data should be performed. Can reduce size of correlation
matrix using risk factors.
VaR : ParameterestimatioN
• Necessary to make distributional assumptions
about assets
historic
price
VaR can be extended to longer-term horizons, but parameters need to be estimated.
Currency hedging can improve return for a given risk exposure.
Hedge calculated during portfolio optimization, should not be treated as separate problem


Risk and Return Performance Attribution for Cross Border Investment Portfolio

Abstract

Similar works

Full text

Available Versions

Mathematics in Industry Information Service Eprints Archive