The implied Sharpe ratio

In an incomplete market, including liquidly traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept—the implied Sharpe ratio—which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.     

Robust performance hypothesis testing with the Sharpe ratio

Applied researchers often test for the difference of the Sharpe ratios of two investment strategies. A very popular tool to this end is the test of Jobson and Korkie [Jobson, J.D. and Korkie, B.M. (1981). Performance hypothesis testing with the Sharpe and Treynor measures. Journal of Finance, 36:889–908], which has been corrected by Memmel [Memmel, C. (2003). Performance hypothesis testing with the Sharpe ratio. Finance Letters, 1:21–23]. Unfortunately, this test is not valid when returns have tails heavier than the normal distribution or are of time series nature. Instead, we propose the use of robust inference methods. In particular, we suggest to construct a studentized time series bootstrap confidence interval for the difference of the Sharpe ratios and to declare the two ratios different if zero is not contained in the obtained interval. This approach has the advantage that one can simply resample from the observed data as opposed to some null-restricted data. A simulation study demonstrates the improved finite sample performance compared to existing methods. In addition, two applications to real data are provided.     

Performance hypothesis testing with the Sharpe ratio: The case of hedge funds

As recent research highlights that the Sharpe ratio has a decision theoretic foundation even in the case of asymmetric or fat-tailed excess returns and thus is adequate even for the evaluation of hedge funds, this note provides the first Sharpe ratio based performance analysis of the hedge fund market. Furthermore, it addresses the important practical question whether the choice of hypothesis test used to statistically compare Sharpe ratios can influence an investor’s hedge fund selection process. Our key findings are as follows: (i) Only a small fraction of hedge funds in our large dataset can significantly outperform passive investments in corresponding hedge fund indices. (ii) Especially in the presence of autocorrelated or skewed excess returns, the traditional test of Jobson and Korkie, 1981, Memmel, 2003 tends to overstate the number of significant outperformers and thus provides potentially misleading information for investors. Decision makers are advised to use the bootstrap test of Ledoit and Wolf (2008) allowing robust and more reliable inference.     

Stock performance by utility indifference pricing and the Sharpe ratio

We compare stock performance based on utility indifference pricing and the Sharpe ratio assuming that stock returns follow the class of discrete normal mixture distributions. The utility indifference price with an exponential utility function satisfies several desirable properties that a suitable value measure should satisfy. For utility indifference pricing, we employ the inner rate of risk aversion proposed by Miyahara [Evaluation of the scale risk. RIMS Kokyuroku, No. 1886, Financial Modeling and Analysis (2013/11/20-2013/11/22), 181–188, 2014], which is the degree of risk aversion that makes the utility indifference price with the exponential utility function zero in order to evaluate stock performance. Using a selection of U.S. stocks, the results show that the evaluation of stock performance based on the inner rate of risk aversion is more relevant for risk-averse investors than that based on the Sharpe ratio, which represents performance by the first two moments.     

Pricing options in incomplete equity markets via the instantaneous Sharpe ratio

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Saá-Requejo (J Polit Econ 108:79–119, 2000) and of Björk and Slinko (Rev Finance 10:221–260, 2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque et al. (Derivatives in financial markets with stochastic volatility. Cambridge University Press, 2000).     

Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino–Satchell and Farinelli–Tibiletti ratios show satisfactorily robustness.     

Risk measurement distortion: an improved model of return smoothing

We examine the effects of smoothed hedge fund returns on standard deviation, skewness, and kurtosis of return and on correlation of returns using a MA(2)-GARCH(1,1)-skewed-t representation instead of the traditional MA(2) model employed in the literature. We present evidence that our proposed representation is more consistent with the behavior of hedge fund returns than the traditional MA(2) representation and that the traditional method tends to overstate the degree of smoothing observed in hedge fund returns. We examine methods for correcting the distortive effects of smoothing using our representation.     

The determinants of the return on index bonds

The investor holding an index-linked bond is guaranteed a given real income irrespective of the prevailing inflation rate. The holding-period return (HPR) on such a bond should, therefore adjust to realized inflation; this is the firsthypothesis tested. The value of the bond may also change due to anticipated changes in the real interest rate which should themselves be related to uncertainty about future inflation; hence HPRs on linked bonds may vary with inflation uncertainty (second hypothesis). Furthermore, for bonds with long periods of time to maturity the effect of uncertainty about future inflation rates may be rather small so that as we approach maturity, the effect of inflation uncertainty should increase (third hypothesis). These three hypotheses are tested on a sample of eight Israeli index-linked bonds with maturities three months apart. The first hypothesis is supported by the data but the last two are not.     

The supraview of return predictive signals

This study seeks to inform investment academics and practitioners by describing and analyzing the population of return predictive signals (RPS) publicly identified over the 40-year period 1970–2010. Our supraview brings to light new facts about RPS, including that more than 330 signals have been reported; the properties of newly discovered RPS are stable over time; and RPS with higher mean returns have larger standard deviations of returns and also higher Sharpe ratios. Using a sample of 39 readily programmed RPS, we estimate that the average cross-correlation of RPS returns is close to zero and that the average correlation between RPS returns and the market is reliably negative. Abstracting from implementation costs, this implies that portfolios of RPS either on their own or in combination with the market will tend to have quite high Sharpe ratios. For academics who seek to document that they have found a genuinely new RPS, we show that the probability that a randomly chosen RPS has a positive alpha after being orthogonalized against five (25) other randomly chosen RPS is 62 % (32 %), suggesting that the returns of a potentially new RPS need to be orthogonalized against the returns of some but not all pre-existing RPS. Finally, we posit that our findings pose a challenge to investment academics in that they imply that either US stock markets are pervasively inefficient, or there exist a much larger number of rationally priced sources of risk in equity returns than previously thought.     

A closer look at return predictability of the US stock market: evidence from new panel variance ratio tests

This paper examines the return predictability of the US stock market using portfolios sorted by size, book-to-market ratio and industry. We use novel panel variance ratio tests, based on the wild bootstrap proposed in this paper, which exhibit desirable size and power properties in small samples. We have found evidence that stock returns have been highly predictable from 1964 to 1996, except for a period leading to the 1987 crash and its aftermath. After 1997, stock returns have been unpredictable overall. At a disaggregated level, we find evidence that large-cap portfolios have been priced more efficiently than small- or medium-cap portfolios; and that the stock returns from high-tech industries are far less predictable than those from non-high-tech industries.     

The return premiums to accruals quality

Using a battery of look-ahead-bias free measures of accruals quality (AQ), we find a strong and long-lasting negative relation between future returns and AQ. In decile portfolios that rank on AQ, a hedge portfolio that goes long in the lowest decile and short in the highest decile generates an annualized, risk-adjusted return of 4–12 % over 1-month to 5-year horizons, depending on the AQ measure and the portfolio weighting scheme. The return premiums associated with AQ are, (1) robust to a wide range of AQ measures, (2) robust to a battery of return-informative variables, and (3) not driven by low-priced or small stocks, earnings shocks, or the fourth-quarter effect. The documented premiums are consistent with the information uncertainty effect where firm uncertainty is negatively related to future returns.     

The return to retail and the performance of US banks

The US banking industry is experiencing a renewed focus on retail banking, a trend often attributed to the stability and profitability of retail activities. This paper examines the impact of banks’ retail intensity on performance from 1997 to 2004 by developing three complementary definitions of retail intensity (retail loan share, retail deposit share, and branches per dollar of assets) and comparing these measures with both equity market and accounting measures of performance. We find that an increased focus on retail banking across US banks is linked with significantly lower equity market and accounting returns for all banks, but lower volatility for only the largest banking companies. We conclude that retail banking may be a relatively stable activity, but it is also a low return one.     

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

We provide an overview of how the law of large numbers breaks down when pricing life‐contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per‐policy risk and show that it goes to a non‐zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non‐systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk.     

The return map: tracking product teams

With a new product, time is now more valuable than money. The costs of conceiving and designing a product are less important to its ultimate success than timeliness to market. One of the most important ways to speed up product development is through interfunctional teamwork. The "Return Map," developed at Hewlett-Packard, provides a way for people from different functions to triangulate on the product development process as a whole. It graphically represents the contributions of all team members to the moment when a project breaks even. It forces the team to estimate and re-estimate the time it will take to perform critical tasks, so that products can get out fast. It subjects the team to the only discipline that works, namely, self-discipline. The map is, in effect, a graph representing time and money, where the time line is divided into three phases: investigation, development, and manufacturing and sales. Meanwhile, costs are plotted against time--as are revenues when they are realized after manufacturing release. Within these points of reference, four novel metrics emerge: Break-Even-Time, Time-to-Market, Break-Even-After-Release, and the Return Factor. All metrics are estimated at the beginning of a project to determine its feasibility, then they are tracked carefully while the project evolves to determine its success. Missed forecasts are inevitable, but managers who punish employees for missing their marks will only encourage them to estimate conservatively, thus building slack into a system meant to eliminate slack. Estimates are a team responsibility, and deviations provide valuable information that spurs continuous investigation and improvement.     

The virtue matrix. Calculating the return on corporate responsibility

Executives who want to make their organizations better corporate citizens face many obstacles: If they undertake costly initiatives that their rivals don't embrace, they risk eroding their company's competitive position. If they invite government oversight, they may be hampered by costly regulations. And if they adopt wage scales and working conditions that prevail in the wealthiest democracies, they may drive jobs to countries with less stringent standards. Such dilemmas call for clear, hard thinking. To aid in that undertaking, Roger Martin introduces the virtue matrix--a tool to help executives analyze corporate responsibility by viewing it as a product or service. The author uses real-life examples to explore the forms and degrees of corporate virtue. He cites Aaron Feuerstein, CEO of Malden Mills, a textile company whose plant was destroyed by fire in 1995. Rather than move operations to a lower-wage region, Feuerstein continued to pay his idled workforce and rebuilt the plant. Unlike the typical CEO of a publicly held corporation, who is accountable to hundreds or thousands of shareholders, Feuerstein was free to act so generously because he had only a few family members to answer to. But as Martin points out, corporations don't operate in a universe composed solely of shareholders. They can be subject to pressure from citizens, employees, and political authorities. The virtue matrix provides a way to assess these forces and how they interact. Martin uses it to examine why the public clamor for more responsible corporate conduct never seems to abate. Another issue the author confronts is anxiety over globalization. Finally, Martin applies the virtue matrix to two crucial questions: What are the barriers to increasing the supply of corporate virtue? And what can companies do to remove those barriers?     

The conditional relation between dispersion and return

The main goal of this paper is to examine the conditional pricing effect of return dispersion on the cross section of returns. We observe a systematic conditional relation between dispersion and return even after controlling for market, size and book-to-market factors. However, we find that return dispersion risk is asymmetrically priced with a significantly positive premium observed during periods of large market gains only. The findings are found to be robust to alternative conditional specifications of market returns, suggesting asymmetric pricing effect of the return dispersion factor. We provide alternative explanations for the systematic risk captured by the return dispersion factor and discuss implications for portfolio management and corporate decisions.