CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTS THE OTHER SIDE OF THE COIN Costs, benefits, optimal exposure Eduardo Walker Professor School of Business Pontificia Universidad Católica de Chile Seminario Internacional FIAP “Perspectivas para la inversión de los fondos de pensiones”, Santiago, Mayo 18-19, 2006

2 Pension funds in EM -- 12% invested abroad Source:

3 Questions Is currency hedging convenient or desirable? –Is the desirability just related to currency volatility? –Should their be a minimum (as for Chilean AFPs)? –How do we assess the costs and benefits of hedging and how do we determine the optimal hedging ratio? Implicit perspective: strategic or policy asset allocation

4 Contents Consequences of a “full hedge” Hedged versus unhedged variances –Explanations for their evolution –Empirical evidence Local investor dilemma: should we hedge? –Global minimum variance portfolio perspective –Unrestricted optimal portfolio perspective Conclusions and caveats

5 Assume we invest in the World equity portfolio, should we hedge the currency risk? ( To hedge or not to hedge…) UNHEDGED return HEDGED return BENEFIT: We recover the risk premium implicit in short term local rates (which should include country and currency risk premia) COST: Does it have a cost? Does it increase risk? –Does hedging increase volatility? (Total risk perspective) –Does hedging increase the risk of our combined portfolio? (Porftolio risk perspective) NO: we have a “free lunch”? YES: we need a context to calibrate costs and benefits

6 var(r L )/var(r) – Local Perspective Var(r L ) –return variance of the MSCI World measured in LC (UNHEDGED) Var(r) –return variance of the MSCI World measured in USD (HEDGED)

7 var(r L )/var(r) (Rolling 60 months)

8

9 What explains the relative variances? var(r L )/var(r) has had huge swings over time in the different countries We can write var(r L ) = var(r+e) = var(r)+var(e)+2cov(r,e) Defining –  e =  cov(r,e)/var(r) “Beta” of exchange rate variations (LC/USD) with respect to the world stock market The “minus” sign is because Beta is in the foreigner’s (USD/LC) perspective We obtain: var(r L )/var(r) = 1 + var(e)/var(r)  2  e So var(r L )/var(r) can change because… –The relative volatility of the exchange rate does, or –The “Beta” of the exchange rate moves Notice the differences in points of view…

10 var(r L )/var(r) = 1 + var(e)/var(r) - 2  e

11 var(r L )/var(r) = 1 + var(e)/var(r) - 2  e

12 Comments In many countries we observe a trend towards higher currency betas with respect to world equity markets –Higher betas lower the volatility benefits of hedging from the perspective of emerging market based investors In Chile, Venezuela and Argentina the volatility of the exchange rate relative to the world stock markets’ has increased In Brazil, Colombia and Mexico, the relative volatility has decreased Hedging increases risk in Chile, Colombia and Mexico Hedging reduces risk in Brazil, Argentina and Venezuela… –…where global equity probably doesn’t make much sense at this point anyway

13 Risk in a Portfolio perspective 1: Global minimum variance portfolios (GMV) measured in the LC of each country Asset classes –Global unhedged equity (MSCI World Index Free) –Global hedged equity Implicit hedge –Local equity (MSCI local indices) Exclude local fixed income which by definition would be (nearly) risk free The question is whether when the GMV includes global equity and if hedging is convenient

14 Portfolio perspective 1: Technical note -- Regression for obtaining Global minimum variance portfolios (GMV) weights The local currency return of a dollar deposit is approximately r F +e L Methodology for estimating Global Minimum Variance portfolio weights using simple regressions, in general: Kempf and Memmel (2003) An advantage is that we don’t need expected return estimates for these results The amount of hedging is implicit –  GL is the total investment in the global portfolio –  PL is the total investment in the local portfolio –1-  PL -  GL is actually minus the hedged fraction

15 Global Minimum Variance Portfolios (GMV) (Evolution of weights, LC perspective)

16 Global Minimum Variance Portfolios (GMV) (Evolution of weights, LC perspective)

17 Lesson from the GMV perspective Most portfolios have positive net investment in dollar deposits –As in negative net hedging But only a few cases are meaningful –Only Chile and Colombia GMVs include positive investment in global equity –In Mexico and Peru GMVs include zero investment in global equity –In Brazil, Argentina and Venezuela GMVs include negative investment in global equity We could have positive hedged global weights and negative unhedged global weights, but the total is negative Frequent home bias Limitation: no one is supposed to purchase the minimum variance portfolio, since it means having infinite risk aversion…

18 Portfolio perspective 2: Unrestricted optimization We assume than an investor is fully invested in local equity portfolio (measured with the MSCI local indices in LC, r P ) We must combine optimally the local equity portfolio with a combination of the hedged and unhedged global equity portfolios (r L * and r L ) –The perspective is always local, measured in LC The optimal combined portfolio is chosen to maximize the Sharpe ratio, from the local perspective:

19 Optimal hedging CHILE

20 Optimal hedging CHILE

21 Optimal hedging COLOMBIA

22 Optimal hedging COLOMBIA

23 Optimal hedging BRAZIL

24 Optimal hedging BRAZIL

25 Conclusions – caveats Concentrate on the perspective of emerging market based investors (EMIs) Currency hedging has costs and bebefits Benefits for EMIs –recover the risk premium in local rates Costs for EMIs –for some countries hedging increases risk Optimal hedging is usually a fraction of the total investment abroad –Could be 100%, or even above –Could be 0%, or even negative From the perspective of a an emerging market investor (EMI), high observed currency betas imply that the foreign currency is a “Natural Hedge” against drops in global (and possibly local) portfolio values –From the perspective of a developed market based investor higher currency betas increase the contribution EM currencies to global portfolio risk Limitations –We implicitly assume that the investment horizon is short and that volatility (and Beta) are adequate measures of risk –Some risks (peso problems) are not well reflected in short-term volatilities –Conclusions may also change if we change the investment horizon

CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTS THE OTHER SIDE OF THE COIN Costs, benefits, optimal exposure Eduardo Walker Professor School of Business Pontificia Universidad Católica de Chile Rio de Janeiro, April 27, 2006

Appendix Examples of hedging and the arithmetics involved

28 A special asset class – hedged foreign portfolio investment Question: what do we obtain if we invest abroad and partially hedge back to local currency the value of our foreign portfolio Necessary information: the forward exchange rate Example: –The initial exchange rate is 34.2 USD/LC (LC is the local currency). –We invested USD1 Mn in the S&P500. The S&P return was 1.5%. –What is the return measured in local currency (LC) if: We did not hedge and the final currency value was 33.5 USD/LC We sell forward USD at 34.3 USD/LC

29 Hedge…

30 Hedge...

31 (1) Result of the partially hedged investment rreturn of the foreign investment, in USD r F USD risk free rate r LF LC risk free rate r L (h)ret. of foreign investment after hedging fraction h of the initial investment, in LC r L = r L (h) with h=0 r L *= r L (h) con h=1+r F r P return of investing in local assets in LC eexchange rate variation (E 1 /E 0 -1), measured as LC per USD

32 (2) From the covered interest rate parity equation… rreturn of the foreign investment, in USD r F USD risk free rate r LF LC risk free rate r L (h)ret. of foreign investment after hedging fraction h of the initial investment, in LC r L = r L (h) with h=0 r L *= r L (h) con h=1+r F r P return of investing in local assets in LC eexchange rate variation (E 1 /E 0 -1), measured as LC per USD

33 (1’) Replacing (2) in (1)… rreturn of the foreign investment, in USD r F USD risk free rate r LF LC risk free rate r L (h)ret. of foreign investment after hedging fraction h of the initial investment, in LC r L = r L (h) with h=0 r L *= r L (h) con h=1+r F r P return of investing in local assets in LC eexchange rate variation (E 1 /E 0 -1), measured as LC per USD

34 (3) Making h = 1+r F … (full hedge) (A fundamental result) rreturn of the foreign investment, in USD r F USD risk free rate r LF LC risk free rate r L (h)ret. of foreign investment after hedging fraction h of the initial investment, in LC r L = r L (h) with h=0 r L *= r L (h) con h=1+r F r P return of investing in local assets in LC eexchange rate variation (E 1 /E 0 -1), measured as LC per USD

35 (3) Then, with h = 1+r F (full hedge)… In terms of volatility, the simplest way of measuring hedging benefits is with the ratio var(r L )/var(r) rreturn of the foreign investment, in USD r F USD risk free rate r LF LC risk free rate r L (h)ret. of foreign investment after hedging fraction h of the initial investment, in LC r L = r L (h) with h=0 r L *= r L (h) con h=1+r F r P return of investing in local assets in LC eexchange rate variation (E 1 /E 0 -1), measured as LC per USD

36 Annualized Standard Deviations S(e): volatility of the exchange rate S(r): volatility of MSCI World S(rp,USD): volatility of local MSCI index in USD S(rp) : volatility of local MSCI index in LC

37 Annualized Standard Deviations S(e): volatility of the exchange rate S(r): volatility of MSCI World S(rp,USD): volatility of local MSCI index in USD S(rp) : volatility of local MSCI index in LC

38 Total risk perspective: Relative Sharpe Ratios Let us assume an international CAPM, with   being the global equity risk premium (assumed at 5.5 percent). –Risk premium in local interest rates (with respect to foreign USD interest rates):  e . Notice that with Beta close to 0.5 the risk premium in local rates is substantial, 2.75%! –Risk premium of the global investment w.r.t. local interest rates without hedge: (1-  e )  –Risk premium obtained with full hedge 

39 Relative Sharpe Ratios

40 Relative Sharpe Ratios

41 Lesson from the total risk perspective Sharpe ratios are generally lower without hedging The possible lower risks of not hedging due to positive betas are more than compensated by: –High relative exchange rate volatility in some cases, and –Not recovering (via hedging) the risk premium in local interest rates Thus, we should hedge… Limitation: we are not considering our entire portfolio –e.g., the contribution of hedging to the risk and return of the local investor’s portfolio

42 eeee Confidence intervals

43 eeee Confidence intervals