Is the January effect still alive in the futures markets?

The January effect concerns the fact that small capitalization stocks have historically outperformed large capitalized stocks in January. We analyze evidence as to whether this anomaly can be exploited in the futures markets as a speculative investment or to add risk-adjusted value to portfolio performance. We find that the January effect is still alive in the futures markets on the Value Line minus S&P 500 spread trade, but that the marginal liquidity of the Value Line stock index futures contract has made it very risky to exploit the effect. Historically from 1982/3 to 2004/5, the trade has been profitable. This anomaly was also exploitable through a Russell 2000 minus S&P 500 spread trade from 1993/4 to 2004/5.

Hedging errors with Leland's option model in the presence of transaction costs

Nonzero transaction costs invalidate the Black–Scholes [1973. Journal of Political Economy 81, 637–654] arbitrage argument based on continuous trading. Leland [1985. Journal of Finance 40, 1283–1301] developed a hedging strategy which modifies the Black–Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Kabanov and Safarian [1997. Finance and Stochastics 1, 239–250] calculated the limiting hedging error of the Leland strategy and pointed out that it is nonzero for the approximate pricing of an European call option, in contradiction to Leland's claim. As a further contribution, we first identify the mathematical flaw in the argument of Leland's claim and then quantify the expected percentage of hedging losses in terms of the hedging frequency and the level of the option strike price.     

Using Tucker’s theorem of the alternative to simplify,review and expand discrete arbitrage theory

For valuing derivatives and other assets in securities and commodities markets, arbitrage pricing theory has been a major approach for decades. This paper derives fundamental arbitrage pricing results in finite dimensions in a simple unified framework using Tucker’s theorem of the alternative. Frictionless results, that is perfect market results, plus imperfect market results such as those with dividends, periodic interest payments, transaction costs, different interest rates for lending and borrowing, shorting costs and constrained short selling are presented. While the results are mostly known and appear in various places, our contribution is to present them in a coherent and comprehensive fashion with very simple proofs. The analysis yields a simple procedure to prove new results and some are presented for cases with imperfect market frictions.     

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.     

Does the bond‐stock earnings yield differential model predict equity market corrections better than high P/E models?

We extend the literature on crash prediction models in three main ways. First, we explicitly relate crash prediction measures and asset pricing models. Second, we present a statistical significance test for crash prediction models. Finally, we propose a definition and a measure of robustness for these models. We apply our statistical test and measure the robustness of selected model specifications of the Price‐Earnings (P/E) ratio and Bond Stock Earning Yield Differential (BSEYD) measures. This analysis shows that the BSEYD and P/E ratios, were statistically significant robust predictors of corrections on the US equity market over the period 1964 to 2014.     

Can Warren Buffett forecast equity market corrections?

Warren Buffett suggested that the ratio of the market value of all publicly traded stocks to the Gross National Product could identify potential overvaluations and undervaluations in the US equity market when this ratio deviates above 120% or below 80%. We investigate whether this ratio is a statistically significant predictor of equity market corrections and rallies. We find that Buffett's decision rule does not deliver satisfactory forecasts. However, when we adopt a time-varying decision rule, the ratio becomes a statistically significant predictor of equity market corrections. The two time-varying decision rules are: (i) predict an equity market correction when the ratio exceeds a 95% one-tail confidence interval based on a normal distribution, and (ii) predict an equity market correction when the ratio exceeds a threshold computed using Cantelli's inequality. These new decision rules are robust to changes in the two key parameters: the confidence level and the forecasting horizon. This paper also shows that the MV/GNP ratio performs relatively well against the four most popular equity market correction models, but the ratio is not a particularly useful predictor of equity market rallies.     

Currency returns, market regimes and behavioral biases

Covered interest rate parity assumes that there is no risk premium on the hedged returns on currencies. However, empirical evidence indicates that risk premiums are not identically zero, and this is referred to as the forward premium puzzle. We show that there exist market regimes, within which behavioral biases affect decisions, and a type of parity holds within regimes. The foreign exchange market switches between regimes where there is a premium. This paper presents various tests for the hypotheses of currency regimes and regime dependent risk premiums. Based on the existence of regimes, a diversified currency portfolio is created with a mean-variance criterion. Using the Federal Exchange Rate Index as a proxy for the currency benchmark and the U.S. T-Bill as the risk free asset, the similarity between the benchmarks and the implied equilibrium hedged and unhedged portfolios provides evidence for regimes and decision bias. Within each regime interest rate parity is appropriate for modeling currency returns.     

Investing in the turn-of-the-year effect

The January effect is concerned with high stock returns in January, especially by small cap stocks. Transactions costs, especially price pressures, make it difficult to take advantage of this anomaly. However, these costs are minimal in the futures markets. This paper discusses the results of small minus large capitalized US stocks since futures trading began in 1982. There is some anticipation of the effect and in the futures markets; the anomaly still exists but is now totally in December.     

On the robustness of the Arrow-Pratt risk aversion measure

For portfolio problems with joint normally distributed asset returns, the risk aversion measure R = -w₀(Eu″(w)/Eu′(w)), where w₀ is initial wealth can be used to characterize optimality. Comparisons between the global measure R and local measures based on R_A = -u″(w)/u′(w) are explored. Simulations for several utility function classes are described.     

Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.