lecture 24: risk premium portfolio diversification risk.pdf · 24: risk premium & portfolio...
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Lectures 24 & 25: Risk
• Lecture 24: Risk Premium & Portfolio Diversification • Bias in the forward exchange market
as a predictor of the future spot exchange rate
• What makes an asset risky?
• The gains from international diversification
• The portfolio balance model
• Appendix: Intervention in the FX Market
• Lecture 25: Sovereign Risk
• Lecture 26 – Possible topics: • Procyclical fiscal policy
• Greece & the euro crisis
• Recent macro history of China ITF220 - Prof.J.Frankel
Does the Forward Market Offer an Unbiased Predictor of the Future Spot Exchange Rate?
ITF220 - Prof.J.Frankel
• More particularly, does the forward discount equal the mathematically expected percentage change in the spot rate:
(fd)t = Et Δst+1 ?
• Given Covered Interest Parity, it is the same as the question whether the interest differential is an unbiased predictor:
(i-i*)t = Et Δst+1 ?
• So then, does the interest differential equal the math-ematically expected percentage change in the spot rate?
Is the interest differential an unbiased predictor of the future spot exchange rate?
• Usual finding: No. Bias is statistically significant: (i-i*)t ≠ Et Δst+1 . .
– In fact, Et Δst+1 is much closer to zero (a random walk).
– The bias supports the “carry trade”:
One can make money, on average, going short in a low-i currency and long in a high-i currency.
• How can this be?
– One interpretation: Rational expectations fails, Δste ≠ EtΔst+1
– Another: Uncovered interest parity fails, i-i*t ≠ Δste
ITF220 - Prof.J.Frankel
A risk premium separates (i-i*)t from Δste
.
In this case, riskier currencies should be the ones to pay higher returns.
What makes an asset risky to a portfolio investor?
• If uncertainty regarding the value of the currency (variance) is high.
• If you already holds a lot of assets in that currency.
• If currency is highly correlated with other assets you hold. What matters is how much risk the currency adds to your overall portfolio.
ITF220 - Prof.J.Frankel
The gains from international diversification
• James Tobin: The theory of optimal portfolio diversification
• “Don’t put all your eggs in one basket.”
• The theory was worked out for stocks in the Capital Asset Pricing Model (CAPM).
• Applies to all assets: bonds, equities; domestic, foreign.
• International markets offer a particular opportunity for diversification, because they move independently to some extent.
ITF220 - Prof.J.Frankel
What portfolio allocation minimizes risk?
• Assume 2 assets (e.g., domestic & foreign), – each with probability ½ of earning -1, ½ of earning +1. – Variance of overall portfolio ≡ Et (overall returnt+1)2
– Assume the 2 assets are uncorrelated.
• If entire portfolio allocated to 1st asset, – Variance = ½ (-1)2 + ½ (+1)2 = 1.
• If entire portfolio allocated to 2nd asset, – Variance = ½ (-1)2 + ½ (+1)2 = 1.
• If portfolio is allocated half to 1st asset & half to 2nd, – Variance = ¼(-1)2 + (½)(0)2 + ¼ (+1)2 = ½ . – That’s minimum-variance. Maximum diversification.
ITF220 - Prof.J.Frankel
Diversification lowers risk to the overall portfolio.
The investor can achieve a lower level of risk by diversifying internationally.
Standard deviation of return to portfolio
ITF220 - Prof.J.Frankel
Investors want to minimize risk and maximize expected return.
• To get them to hold assets that add risk to the portfolio, you have to offer them a higher expected return.
• That is why stocks pay a higher expected return than treasury bills.
• Do foreign assets pay a higher expected return than domestic assets?
ITF220 - Prof.J.Frankel
Placing 20% of your portfolio abroad reduces risk (diversification). After that point, the motive for going abroad is higher expected return;
investors who are more risk averse won’t go much further.
Risk →
↑ Return
Medium risk- aversion
High risk- aversion
Low risk- aversion
Purely US
ITF220 - Prof.J.Frankel
Similarly, putting 25% of the global portfolio
in emerging markets gives diversification.
Risk →
↑ Return
After that, the gain in expected return
comes at the expense of higher risk.
ITF220 - Prof.J.Frankel
The Portfolio Balance Model • Portfolio investors should allocate shares in their portfolios to countries’ assets as: - a decreasing function of the asset’s risk, and - an increasing function of its expected rate of return (risk premium).
• Valuation effect in fx: a 1% increase in supply of $ assets (whether in the form of money or not) can be offset by a 1% depreciation, -- so that portfolio share is unchanged, and
-- therefore no need to increase expected return to attract demand.
• Another implication: => FX intervention can have an effect even if sterilized.
• One implication: As its debt grows, a deficit country will eventually experience depreciation of its currency, or its interest rate will be forced up, or both.
ITF220 - Prof.J.Frankel
APPENDIX: Intervention in the foreign exchange market
• was effective in 1985, to bring down the $, represented by the G-5 agreement at the Plaza Hotel;
• and was effective at times subsequently (though not always).
• Since 2001, the ECB, Fed, & BoJ have intervened very little;
• In 2013 the G-7 agreed not to intervene, – to avoid currency wars.
• But other floaters intervene more often, – Esp., major emerging market countries,
ITF220 - Prof.J.Frankel
US FX intervention, even though sterilized, can sometimes be effective: The Plaza Accord of 1985 brought the dollar down,
and the G-7 meeting of 1995 brought it up.
1985-1999
ITF220 - Prof.J.Frankel
Managed float (“leaning against the wind”):
Kaushik Basu & Aristomene Varoudakis, Policy RWP 6469, World Bank, 2013, “How to Move the Exchange Rate If You Must: The Diverse Practice of Foreign Exchange Intervention by Central Banks and a Proposal for Doing it Better” May, p. 14
Turkey’s central bank buys lira when it depreciates, and sells when it is appreciates.