1. Lecture 26: Exchange Risk & 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

2. Does the forward market offer an unbiased predictor of the future spot exchange rate?
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?
Prof.J.Frankel

3. 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 (s is 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
Because a risk premium separates (i-i*)t from Δste .
In this case, riskier currencies should be the ones to pay higher returns.
Prof.J.Frankel

4. 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.
Prof.J.Frankel

5. 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.
Prof.J.Frankel

6. 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) ½ (+1)2 = 1.
If entire portfolio allocated to 2nd asset,
Variance = ½ (-1) 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.
Prof.J.Frankel

7. Diversification lowers risk to the overall portfolio.
Standard
deviation
of return to portfolio
Diversification lowers risk to the overall portfolio.
The investor can achieve a lower level of risk by diversifying internationally.
Prof.J.Frankel

8. 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?
Prof.J.Frankel

9. ↑ Return
Low risk- aversion
Medium risk aversion
High risk- aversion
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.
Purely US
Risk →
Prof.J.Frankel

10. ↑ Return Risk → After that, the gain in expected return
comes at the expense of higher risk.
Similarly, putting 25% of the global portfolio
in emerging markets gives diversification.
Risk →
Prof.J.Frankel

11. 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.
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.
Another implication: => FX intervention can have an effect even if sterilized.
Prof.J.Frankel

12. Professor Jeffrey Frankel, Harvard Kennedy School

13. 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 sometimes subsequently.
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,
Prof.J.Frankel

14. Managed float (“leaning against the wind”):
Turkey’s central bank buys lira when it depreciates, and sells when it is appreciates.
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
Prof.J.Frankel