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CURRENCY HEDGING AND GLOBAL PORTFOLIO INVESTMENTS THE OTHER SIDE OF THE COIN Costs, benefits, optimal exposure PowerPoint Presentation
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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 ewalker@faceapuc.cl

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slide1

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

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

questions
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
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
slide5
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 r l var r local perspective
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
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
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
slide13
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
slide14
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
lesson from the gmv 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
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:
optimal hedging chile

Global risk premium

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 CHILE
optimal hedging colombia

Global risk premium

5.50%

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 COLOMBIA
optimal hedging brazil

Global risk premium

5.50%

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 BRAZIL
conclusions caveats
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
slide26

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

Eduardo Walker

Professor

School of Business

Pontificia Universidad Católica de Chile

ewalker@faceapuc.cl

Rio de Janeiro, April 27, 2006

appendix

Appendix

Examples of hedging and the arithmetics involved

a special asset class hedged foreign portfolio investment
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
(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
(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
(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 r f full hedge a fundamental result
(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 r f full hedge
(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
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 deviations37
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
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
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
slide42
be

Confidence intervals

slide43
be

Confidence intervals