Volatility‐Managed Portfolios

Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean‐variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting‐against‐beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk‐based explanations and is a challenge to structural models of time‐varying expected returns.     

(Almost) Model‐Free Recovery

Under mild assumptions, we recover the model‐free conditional minimum variance projection of the pricing kernel on various tradeable realized moments of market returns. Recovered conditional moments predict future realizations and give insight into the cyclicality of equity premia, variance risk premia, and the highest attainable Sharpe ratios under the minimum variance probability. The pricing kernel projections are often U‐shaped and give rise to optimal conditional portfolio strategies with plausible market timing properties, moderate countercyclical exposures to higher realized moments, and favorable out‐of‐sample Sharpe ratios.     

Modeling Corporate Bond Returns

We propose a conditional factor model for corporate bond returns with five factors and time-varying factor loadings. We have three main empirical findings. First, our factor model excels in describing the risks and returns of corporate bonds, improving over previously proposed models in the literature by a large margin. Second, our model recommends a systematic bond investment portfolio whose high out-of-sample Sharpe ratio suggests that the credit risk premium is notably larger than previously estimated. Third, we find closer integration between debt and equity markets than found in prior literature.     

Does the choice of performance measure influence the evaluation of hedge funds?

The Sharpe ratio is adequate for evaluating investment funds when the returns of those funds are normally distributed and the investor intends to place all his risky assets into just one investment fund. Hedge fund returns differ significantly from a normal distribution. For this reason, other performance measures for hedge fund returns have been proposed in both the academic and practice-oriented literature. In conducting an empirical study based on return data of 2763 hedge funds, we compare the Sharpe ratio with 12 other performance measures. Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.     

Complex Asset Markets

Investors' individual arbitrage models introduce idiosyncratic risk into complex asset strategies, driving up average returns and Sharpe ratios. However, despite the attractive risk-return trade-off, participation is limited. This is because effective Sharpe ratios in complex asset markets vary with investors' expertise. Investors with higher expertise, better models, and lower resulting idiosyncratic risk exposures realize higher Sharpe ratios. Their demand deters entry by less sophisticated investors. As predicted by our model, market dislocations are characterized by an increase in idiosyncratic risk, investor exit, and persistently elevated alphas and Sharpe ratios. The selection effect from higher expertise agents' more favorable Sharpe ratios is unique to our model and key to our main results.     

The Effect of Lender Identity on a Borrowing Firm's Equity Return

Previous research demonstrates that a firm's common stock price tends to fall when it issues new public securities. By contrast, commercial bank loans elicit significantly positive borrower returns. This article investigates whether the lender's identity influences the market's reaction to a loan announcement. Although we find no significant difference between the market's response to bank and nonbank loans, we do find that lenders with a higher credit rating are associated with larger abnormal borrower returns. This evidence complements earlier findings that an auditor's or investment banker's perceived “quality” signals valuable information about firm value to uninformed market investors.     

Statistical arbitrage in the US equities market

We study model-driven statistical arbitrage in US equities. Trading signals are generated in two ways: using Principal Component Analysis (PCA) or regressing stock returns on sector Exchange Traded Funds (ETFs). In both cases, the idiosyncratic returns are modelled as mean-reverting processes, which leads naturally to ‘contrarian’ strategies. We construct, back-test and compare market-neutral PCA- and ETF-based strategies applied to the broad universe of US equities. After accounting for transaction costs, PCA-based strategies have an average annual Sharpe ratio of 1.44 over the period 1997 to 2007, with stronger performances prior to 2003. During 2003–2007, the average Sharpe ratio of PCA-based strategies was only 0.9. ETF-based strategies had a Sharpe ratio of 1.1 from 1997 to 2007, experiencing a similar degradation since 2002. We also propose signals that account for trading volume, observing significant improvement in performance in the case of ETF-based signals. ETF-strategies with volume information achieved a Sharpe ratio of 1.51 from 2003 to 2007. The paper also relates the performance of mean-reversion statistical arbitrage strategies with the stock market cycle. In particular, we study in detail the performance of the strategies during the liquidity crisis of the summer of 2007, following Khandani and Lo [Social Science Research Network (SSRN) working paper, 2007].     

Global style momentum

We first document the empirical regularity of significant style-level momentum returns in international data. Then we test some Barberis and Shleifer (2003) propositions regarding style momentum. One proposition holds that Sharpe ratios from style-level momentum strategies should be at least as large as stock-level momentum Sharpe ratios. We test for style-level momentum profitability in our sample of global markets and find some evidence of larger style momentum Sharpe ratios, especially within the value-growth style. However, most of the evidence favors stock momentum. The Barberis and Shleifer (2003) model also suggests that style momentum could be time-varying. Variables that effectively condition stock momentum are much less effective with style momentum.     

Normative portfolio theory

In this paper, we correct the adverse impact of estimation risk on both portfolio weights and performance with two new equity allocation methods we implement with estimation-free and estimated ex-ante returns. Portfolios with estimation-free ex-ante returns and systematic-to-unsystematic risk weights have statistically higher Sharpe ratios than both similar portfolios with estimated ex-ante returns and 1/N′th portfolios. Optimal portfolio methods with well-behaved weights guide investors in a way not hitherto possible (normative portfolio theory).     

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.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets

The paper presents an incomplete market pricingmethodology generating asset pricebounds conditional on the absence of attractiveinvestment opportunities in equilibrium.The paper extends and generalises the seminal article ofCochrane and Saá-Requejowho pioneered option pricing based on the absenceof arbitrage and high Sharpe Ratios. Ourcontribution is threefold:We base the equilibrium restrictions on an arbitrary utility function, obtaining theCochrane and Saá-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms ofGeneralised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide aconsistent ranking of investment opportunities even when asset returns are highlynon-normal. Last but not least, we demonstrate that for Itô processes theCochrane and Saá-Requejo price bounds are invariant to the choice of the utilityfunction, and that in the limit they tend to a unique price determined by theminimal martingale measure.     

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.     

Benchmarking the performance of recommended allocations to equities,bonds, and cash by international investment houses

We conduct performance tests of the recommended asset allocations made by a panel of international investment houses (the “Houses”) from 1982 through 2005. We compare the returns and Sharpe Ratios from the recommended-weight portfolio against those of several benchmark portfolios and to a set of 10,000 returns and Sharpe Ratios from randomly shuffled-weight and shuffled-weight change portfolios. We find that the Houses generally fail to outperform the benchmarks. The shuffled-weight change benchmark exhibits a robust “style-preserving” property in that the average portfolio standard deviation is nearly equal to the portfolio standard deviation from the actual recommended weights.     

Time-varying risk premia and the cost of capital: An alternative implication of the Q theory of investment

Evidence suggests that expected excess stock market returns vary over time, and that this variation is much larger than that of expected real interest rates. It follows that a large fraction of the movement in the cost of capital in standard investment models must be attributable to movements in equity risk-premia. In this paper we emphasize that such movements in equity risk premia should have implications not merely for investment today, but also for future investment over long horizons. In this case, predictive variables for excess stock returns over long-horizons are also likely to forecast long-horizon fluctuations in the growth of marginal Q, and therefore investment. We test this implication directly by performing long-horizon forecasting regressions of aggregate investment growth using a variety of predictive variables shown elsewhere to have forecasting power for excess stock market returns.     

Statistical arbitrage with optimal causal paths on high-frequency data of the S&P 500

This paper develops the optimal causal path algorithm and applies it within a fully-fledged statistical arbitrage framework to minute-by-minute data of the S&P 500 constituents from 1998 to 2015. Specifically, the algorithm efficiently determines the optimal non-linear mapping and the corresponding lead–lag structure between two time series. Afterwards, this study explores the use of optimal causal paths as a means for identifying promising stock pairs and for generating buy and sell signals. For this purpose, the established trading strategy exploits information about the leading stock to predict future returns of the following stock. The value-add of the proposed framework is assessed by benchmarking it with variants relying on classic similarity measures and a buy-and-hold investment in the S&P 500 index. In the empirical back-testing study, the trading algorithm generates statistically and economically significant returns of 54.98% p.a. and an annualized Sharpe ratio of 3.57 after transaction costs. Returns are well superior to the benchmark approaches and do not load on any common sources of systematic risk. The strategy outperforms in the context of cryptocurrencies even in recent times due to the fact that stock returns contain substantial information about the future bitcoin returns.     

Zur Risikoanalyse von Hedgefonds: Ein datenanalytischer Ansatz

Hedge fund returns have a number of specific features compared to traditional investments which result in problems when applying traditional methods of risk analysis (Markowitz portfolio selection theory, Sharpe Ratio, value at risk calculation based on normal returns). These problems have to be considered adequately by insurance companies when constructing internal risk models and performing risk management for hedge funds in their investment.The present paper has its focus on the departure of hedge fund returns from the normality hypothesis, especially with respect to the statistical quantities skewness and kurtosis (fat tail problem). A statistical analysis of hedge fund index returns gives evidence that the majority of hedge fund returns show substantial departures from normality. In addition, the analysis shows that hedge fund returns are adequately represented by the family of GH-distributions developed in exploratory data analysis. Following this result a risk analysis of hedge fund strategies is performed on the basis of the GH-value at risk.     

Crash-neutral currency carry trades

Currency carry trades exploiting violations of uncovered interest rate parity in G10 currencies deliver significant excess returns with annualized Sharpe ratios equal to or greater than those of equity market factors (1990–2012). Using data on out-of-the-money foreign exchange options, I compute returns to crash-hedged portfolios and demonstrate that the high returns to carry trades are not due to peso problems. A comparison of the returns to hedged and unhedged trades indicates crash risk premia account for at most one-third of the excess return to currency carry trades.     

A stochastic dominance analysis of yen carry trades

Yen carry trades have made headline news for over a decade. We examine the profitability of such trades for the period 2001–2009. Yen carry trades generated high mean returns and Sharpe ratios prior to the recent financial crisis. They continued to outperform major stock markets for the full sample period. Given the non-normality of carry trade returns, we apply non-parametric tests based on stochastic dominance (SD) to evaluate whether the high returns of yen carry trades are compatible with risk as reflected in returns on US and global stock market indices. We apply a general test for SD developed recently by Linton, Maasoumi and Whang (2005) to six currencies as well as portfolios of these currencies. For a large class of risk-averse investors, profits from yen carry trades cannot be attributed to risks.     

Analysing the performance of managed funds using the wavelet multiscaling method

We propose a new approach for investigating the performance of managed funds using wavelet analysis and apply it to an Australian dataset. This method, applied to a multihorizon Sharpe ratio, shows that the wavelet variance at the short scale is higher than that of the longer scale, implying that an investor with a short investment horizon has to respond to every fluctuation in the realized returns, while for an investor with a much longer horizon, the long-run risk associated with unknown expected returns is not as important as the short-run risk. Using multihorizon Sharpe ratios of six groups of managed funds, we find that none of the fund groups are dominant over all time scales.