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The role of index bonds in universal currency hedging

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  • Ryle Perera

Abstract

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.

Suggested Citation

  • Ryle Perera, 2000. "The role of index bonds in universal currency hedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 271-284.
    • Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:271-284
    DOI: 10.1080/13504860110058035
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    References listed on IDEAS

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    1. Fischer, Stanley, 1975. "The Demand for Index Bonds," Journal of Political Economy, University of Chicago Press, vol. 83(3), pages 509-534, June.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Adler, Michael & Prasad, Bhaskar, 1992. "On Universal Currency Hedges," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(1), pages 19-38, March.
    4. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    5. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    6. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, October.
    7. Black, Fischer, 1990. "Equilibrium Exchange Rate Hedging," Journal of Finance, American Finance Association, vol. 45(3), pages 899-907, July.
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    Cited by:

    1. Peters, David W., 2007. "The behavior of government of Canada real return bond returns," International Review of Financial Analysis, Elsevier, vol. 16(2), pages 152-171.

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