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CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTS THE OTHER SIDE OF THE COIN Costs, benefits, optimal exposure

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### CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTSTHE OTHER SIDE OF THE COINCosts, benefits, optimal exposure

### CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTSTHE OTHER SIDE OF THE COINCosts, benefits, optimal exposure

### Appendix

Eduardo Walker

Professor

School of Business

Pontificia Universidad Católica de Chile

ewalker@faceapuc.cl

Seminario Internacional FIAP “Perspectivas para la inversión de los fondos de pensiones”, Santiago, Mayo 18-19, 2006

Pension funds in EM-- 12% invested abroad

Source: www.fiap.cl

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

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

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

var(rL)/var(r) – Local Perspective

- Var(rL)
- return variance of the MSCI World measured in LC (UNHEDGED)
- Var(r)
- return variance of the MSCI World measured in USD (HEDGED)

What explains the relative variances?

- var(rL)/var(r) has had huge swings over time in the different countries
- We can write var(rL) = var(r+e) = var(r)+var(e)+2cov(r,e)
- Defining
- be = -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(rL)/var(r) = 1 + var(e)/var(r) - 2be
- So var(rL)/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…

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

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

Portfolio perspective 1:Technical note -- Regression for obtaining Global minimum variance portfolios (GMV) weights

- The local currency return of a dollar deposit is approximately rF+eL
- 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
- bGL is the total investment in the global portfolio
- bPL is the total investment in the local portfolio
- 1- bPL-bGL is actually minus the hedged fraction

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

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

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…

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, rP)
- We must combine optimally the local equity portfolio with a combination of the hedged and unhedged global equity portfolios (rL* and rL)
- The perspective is always local, measured in LC
- The optimal combined portfolio is chosen to maximize the Sharpe ratio, from the local perspective:

5.50%

Local risk premium

5.50%

Local currency beta

0

0.1

0.3

0.5

Global premium unhedged

5.50%

4.95%

3.85%

2.75%

P

A

weight

N

MSCI-W unhedged (rL)

79.99%

67.95%

36.27%

-12.30%

E

MSCI-W hedged (r )

2.60%

12.02%

36.82%

74.85%

L

Total foreign

82.59%

79.97%

73.09%

62.54%

MSCI Chile (r

)

17.41%

20.03%

26.91%

37.46%

p

A

Global risk premium

5.50%

Local risk premium

6.50%

Local currency beta

0

0.1

0.3

0.5

P

Global premium hedged

5.50%

4.95%

3.85%

2.75%

A

N

weight

MSCI-W unhedged (rL)

E

75.75%

63.75%

32.49%

-14.60%

MSCI-W hedged (r )

L

-3.87%

4.69%

27.02%

60.65%

Total foreign

71.87%

68.45%

59.51%

46.05%

B

MSCI Chile (rp )

28.13%

31.55%

40.49%

53.95%

Optimal hedging CHILE5.50%

Local risk premium

5.50%

Local currency beta

0

0.1

0.3

0.5

P

Global premium unhedged

5.50%

4.95%

3.85%

2.75%

A

weight

N

MSCI-W unhedged (rL)

93.51%

72.18%

12.91%

-88.01%

E

MSCI-W hedged (r )

-3.76%

16.59%

73.15%

169.45%

L

Total foreign

89.75%

88.77%

86.06%

81.45%

MSCI Colombia (r

)

10.25%

11.23%

13.94%

18.55%

p

A

Global risk premium

5.50%

Local risk premium

6.50%

Loca currency beta

P

0

0.1

0.3

0.5

Global premium unhedged

A

5.50%

4.95%

3.85%

2.75%

N

weight

E

MSCI-W unhedged (rL)

91.93%

70.88%

12.77%

-84.78%

L

MSCI-W hedged (r )

-5.72%

14.02%

68.51%

159.97%

Total foreign

86.21%

84.90%

81.27%

75.19%

B

MSCI Colombia (rp )

13.79%

15.10%

18.73%

24.81%

Optimal hedging COLOMBIA5.50%

Local risk premium

5.50%

Local currency beta

0

0.1

0.3

0.5

P

Global premium unhedged

5.50%

4.95%

3.85%

2.75%

A

weight

N

MSCI-W unhedged (rL)

36.59%

33.98%

28.11%

21.20%

E

MSCI-W hedged (r )

66.14%

69.29%

76.34%

84.66%

L

Total foreign

102.74%

103.27%

104.46%

105.86%

MSCI Brazil (r

)

-2.74%

-3.27%

-4.46%

-5.86%

p

A

Global risk premium

5.50%

Local risk premium

6.50%

Local currency beta

P

0

0.1

0.3

0.5

Global premium unhedged

A

5.50%

4.95%

3.85%

2.75%

N

weight

MSCI-W unhedged (rL)

E

37.53%

34.94%

29.12%

22.25%

MSCI-W hedged (r )

L

57.98%

60.83%

67.23%

74.78%

Total foreign

95.51%

95.76%

96.34%

97.02%

B

MSCI Brazil (rp )

4.49%

4.24%

3.66%

2.98%

Optimal hedging BRAZILConclusions – 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

Eduardo Walker

Professor

School of Business

Pontificia Universidad Católica de Chile

ewalker@faceapuc.cl

Rio de Janeiro, April 27, 2006

Examples of hedging and the arithmetics involved

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 USD1000000 at 34.3 USD/LC

(1) Result of the partially hedged investment

- r return of the foreign investment, in USD
- rF USD risk free rate
- rLF LC risk free rate
- rL(h) ret. of foreign investment after hedging fraction h of the initial investment, in LC
- rL = rL(h) with h=0
- rL* = rL(h) con h=1+rF
- rP return of investing in local assets in LC
- e exchange rate variation (E1/E0-1), measured as LC per USD

(2) From the covered interest rate parity equation…

- r return of the foreign investment, in USD
- rF USD risk free rate
- rLF LC risk free rate
- rL(h) ret. of foreign investment after hedging fraction h of the initial investment, in LC
- rL = rL(h) with h=0
- rL* = rL(h) con h=1+rF
- rP return of investing in local assets in LC
- e exchange rate variation (E1/E0-1), measured as LC per USD

(1’) Replacing (2) in (1)…

- r return of the foreign investment, in USD
- rF USD risk free rate
- rLF LC risk free rate
- rL(h) ret. of foreign investment after hedging fraction h of the initial investment, in LC
- rL = rL(h) with h=0
- rL* = rL(h) con h=1+rF
- rP return of investing in local assets in LC
- e exchange rate variation (E1/E0-1), measured as LC per USD

(3) Making h = 1+rF… (full hedge)(A fundamental result)

- r return of the foreign investment, in USD
- rF USD risk free rate
- rLF LC risk free rate
- rL(h) ret. of foreign investment after hedging fraction h of the initial investment, in LC
- rL = rL(h) with h=0
- rL* = rL(h) con h=1+rF
- rP return of investing in local assets in LC
- e exchange rate variation (E1/E0-1), measured as LC per USD

(3) Then, with h = 1+rF (full hedge)…

- In terms of volatility, the simplest way of measuring hedging benefits is with the ratio var(rL)/var(r)
- r return of the foreign investment, in USD
- rF USD risk free rate
- rLF LC risk free rate
- rL(h) ret. of foreign investment after hedging fraction h of the initial investment, in LC
- rL = rL(h) with h=0
- rL* = rL(h) con h=1+rF
- rP return of investing in local assets in LC
- e exchange rate variation (E1/E0-1), measured as LC per USD

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

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

Total risk perspective: Relative Sharpe Ratios

- Let us assume an international CAPM, with F being the global equity risk premium (assumed at 5.5 percent).
- Risk premium in local interest rates (with respect to foreign USD interest rates): beF.
- 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-be)F
- Risk premium obtained with full hedgeF

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

be

Confidence intervals

be

Confidence intervals

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