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Implied betas for the Frankel–Wei regression framework

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  • Kunkler, Michael

Abstract

The Frankel–Wei regression framework measures the relationship between one currency and another currency solely by using foreign exchange rates as regression variables, where investors choose a common numéraire for the foreign exchange rates. When the common numéraire is a single currency, the foreign exchange rates are bilateral exchange rates. Option implied volatilities are easily estimated from listed option prices for bilateral exchange rates. In this paper, we use the implied volatilities to estimate implied betas for the Frankel–Wei regression framework. We show that the average beta and the average implied beta are both exactly 0.5, for each currency in a system of currencies.

Suggested Citation

  • Kunkler, Michael, 2022. "Implied betas for the Frankel–Wei regression framework," Economics Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:ecolet:v:218:y:2022:i:c:s0165176522002713
    DOI: 10.1016/j.econlet.2022.110758
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    References listed on IDEAS

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    1. Kunkler, Michael, 2022. "Using the Special Drawing Right in the Frankel-Wei regression framework," Finance Research Letters, Elsevier, vol. 46(PB).
    2. Jose A. Lopez & Christian Walter, 1997. "Is implied correlation worth calculating? Evidence from foreign exchange options and historical data," Research Paper 9730, Federal Reserve Bank of New York.
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    4. Kunkler, Michael, 2021. "The Chinese renminbi's co-movement with the US dollar: Addressing the numéraire issue," Finance Research Letters, Elsevier, vol. 40(C).
    5. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    6. Jeffrey A. Frankel & Shang-Jin Wei, 1994. "Yen Bloc or Dollar Bloc? Exchange Rate Policies of the East Asian Economies," NBER Chapters, in: Macroeconomic Linkage: Savings, Exchange Rates, and Capital Flows, pages 295-333, National Bureau of Economic Research, Inc.
    7. Campa, Jose Manuel & Chang, P. H. Kevin, 1998. "The forecasting ability of correlations implied in foreign exchange options," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 855-880, December.
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    More about this item

    Keywords

    Exchange rates; Implied volatilities; Implied betas;
    All these keywords.

    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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