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The Risk Return Tradeoff in the Long Run: 1836–2003

Christian Lundblad Journal of Financial Economicsvol. 85, no. 1 (July 2007):123–150

Although the risk–return trade-off is fundamental to finance, the empirical literature has offered mixed results. The author extends the sample considerably and analyzes nearly two centuries of both U.S. and U.K. market returns and finds a positive and statistically significant risk–return trade-off in line with the postulated theory.

Previous attempts at studying the risk–return trade-off have typicallyused the past 50–75 years of data along with the popular generalizedautoregressive conditional heteroscedasticity in-mean (GARCH-M)framework. The evidence suggests that the relationship is weak at bestand is particularly sensitive to the volatility specification. The authorargues that within the GARCH-M framework, one needs a very largeamount of data to successfully detect the risk–return trade-off.

The author starts with a Monte Carlo analysis on the small sampledistribution of the risk–return trade-off coefficient. In the simulation,expected returns are driven by conditional volatility by constructionand realized return variation is calibrated to be nearly unrelated tovolatility (as in the real data). This analysis is done for the GARCH-Mand TARCH (threshold ARCH) specifications. It is conducted forsimulated sample sizes of 500, 2,000, and 5,000. The author considerssensitivity of the results to the level of return volatility—the volatilityof return volatility—and the persistence of return. He then considerswhether one can improve the precision by using high-frequency datarather than long data spans.

Returns from 1836 to 1925 are obtained from data compiled bySchwert (Journal of Business, 1990), and for the 1926–2003 period,

Christian Lundblad is at the University of North Carolina at Chapel Hill. Thesummary was prepared by Yazann S. Romahi, CFA, JPMorgan Asset Management.

Equity Investments • 53

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CRSP value-weighted portfolio returns for the NYSE, Amex, andNASDAQ markets are used. Data are also obtained for the UnitedKingdom from Global Financial Data.

In analyzing the historical data, the author uses the same frameworkbut with a number of different variance specifications: GARCH,EGARCH, TARCH, and QGARCH. The latter three specificationsenable the evaluation of the importance of leverage-effect asymmetryand its implication for the empirical risk–return trade-off. Timevariation of the risk–return trade-off is also examined. In particular,the relationship with the development of the financial market (marketcapitalization/GDP), macroeconomic liquidity (M3/GDP), reces-sions, and the overall state of the economy (foreign trade [exports plusimports/GDP] and size of government [GOV/GDP]) are considered.

The author finds that with a sample size of 500 and with the risk–return trade-off coefficient known to be 2, 19 percent (22 percent)of the time for the GARCH (TARCH) specification, the estimatedcoefficient is negative. If the sample size is increased to 2,000, thisfigure falls dramatically, to 3 percent (7 percent), and it falls to lessthan 1 percent for 5,000 observations. Moreover, the author findsthat the conditional probability of estimating a negative coefficientover a short period when the longer sample yields a correct positiveestimate is 28 percent.

The author also finds that the ability to detect the risk–return trade-off is closely linked to the magnitude and volatility of return volatility.Doubling (halving) return volatility yields a negative estimate 35percent (6 percent) of the time instead of 19 percent. Doublingvolatility of volatility results in a negative estimate only 5 percent ofthe time. By analyzing the different frequencies, the author finds thatthe distribution of the estimate is almost identical, suggesting thatgoing to higher frequencies yields no improvement whereas longerdata spans yield significant improvement.

In examining the historical U.S. long-term data, the author finds apositive trade-off, with the risk premium ranging from 5.2 percent to7.1 percent for all four volatility specifications examined. Whenconsidering individual subperiods, given the small sample size, anumber of the estimates are negative, including the postwar period.

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2008, CFA Institute

For robustness, U.K. data are also considered. The postwar period forthe United Kingdom yields a positive but statistically insignificantestimate. This suggests that the negative postwar result obtained forthe U.S. data is a result of sampling error. Over the long period, hefinds the result to be around 2, as in the U.S. data.

The exploratory evidence suggests that the risk–return trade-off isrelated to recessions, the overall size of the equity market, externaltrade, and government spending.

Keywords: Equity Investments: fundamental analysis and valuation models;Investment Theory: CAPM, APT, and other pricing theories; Risk Measurement andManagement: equity portfolios