**Treynor Measure**

Jack L. Treynor was the first to provide investors with a composite measure of portfolio performance that also included risk. Treynor's objective was to find a performance measure that could apply to all investors, regardless of their personal risk preferences. He suggested that there were really two components of risk: the risk produced by fluctuations in the stock market and the risk arising from the fluctuations of individual securities.

Treynor introduced the concept of the security market line, which defines the relationship between portfolio returns and market rates of returns, whereby the slope of the line measures the relative volatility between the portfolio and the market (as represented by beta). The beta coefficient is simply the volatility measure of a stock portfolio to the market itself. The greater the line's slope, the better the risk-return tradeoff.

The Treynor measure, also known as the reward-to-volatility ratio, can be easily defined as:

(Portfolio Return – Risk-Free Rate) / Beta

The numerator identifies the risk premium and the denominator corresponds with the risk of the portfolio. The resulting value represents the portfolio's return per unit risk.

To better understand how this works, suppose that the 10-year annual return for the S&P 500 (market portfolio) is 10%, while the average annual return on Treasury bills (a good proxy for the risk-free rate) is 5%. Then assume you are evaluating three distinct portfolio managers with the following 10-year results:

Managers Average Annual Return Beta

Manager A 10% 0.90

Manager B 14% 1.03

Manager C 15% 1.20

Now, you can compute the Treynor value for each:

T(market) = (.10-.05)/1 = .05

T(manager A) = (.10-.05)/0.90 = .056

T(manager B) = (.14-.05)/1.03 = .087

T(manager C) = (.15-.05)/1.20 = .083

The higher the Treynor measure, the better the portfolio. If you had been evaluating the portfolio manager (or portfolio) on performance alone, you may have inadvertently identified manager C as having yielded the best results. However, when considering the risks that each manager took to attain their respective returns, Manager B demonstrated the better outcome. In this case, all three managers performed better than the aggregate market.

Because this measure only uses systematic risk, it assumes that the investor already has an adequately diversified portfolio and, therefore, unsystematic risk (also known as diversifiable risk) is not considered. As a result, this performance measure should really only be used by investors who hold diversified portfolios.

**Sharpe Ratio**

The Sharpe ratio is almost identical to the Treynor measure, except that the risk measure is the standard deviation of the portfolio instead of considering only the systematic risk, as represented by beta. Conceived by Bill Sharpe, this measure closely follows his work on the capital asset pricing model (CAPM) and by extension uses total risk to compare portfolios to the capital market line.

The Sharpe ratio can be easily defined as:

(Portfolio Return – Risk-Free Rate) / Standard Deviation

Using the Treynor example from above, and assuming that the S&P 500 had a standard deviation of 18% over a 10-year period, let's determine the Sharpe ratios for the following portfolio managers:

Manager Annual Return Portfolio Standard Deviation

Manager X 14% 0.11

Manager Y 17% 0.20

Manager Z 19% 0.27

S(market) = (.10-.05)/.18 = .278

S(manager X) = (.14-.05)/.11 = .818

S(manager Y) = (.17-.05)/.20 = .600

S(manager Z) = (.19-.05)/.27 = .519

Once again, we find that the best portfolio is not necessarily the one with the highest return. Instead, it's the one with the most superior risk-adjusted return, or in this case the fund headed by manager X.

Unlike the Treynor measure, the Sharpe ratio evaluates the portfolio manager on the basis of both rate of return and diversification (as it considers total portfolio risk as measured by standard deviation in its denominator). Therefore, the Sharpe ratio is more appropriate for well-diversified portfolios, because it more accurately takes into account the risks of the portfolio.

**Jensen Measure / Alpha**

Like the previous performance measures discussed, the Jensen measure is also based on CAPM. Named after its creator, Michael C. Jensen, the Jensen measure calculates the excess return that a portfolio generates over its expected return. This measure of return is also known as alpha.

The Jensen ratio measures how much of the portfolio's rate of return is attributable to the manager's ability to deliver above-average returns, adjusted for market risk. The higher the ratio, the better the risk-adjusted returns. A portfolio with a consistently positive excess return will have a positive alpha, while a portfolio with a consistently negative excess return will have a negative alpha.

The formula is broken down as follows:

Jensen\'s Alpha = Portfolio Return – Benchmark Portfolio Return

Where: Benchmark Return (CAPM) = Risk-Free Rate of Return + Beta (Return of Market – Risk-Free Rate of Return)

So, if we once again assume a risk-free rate of 5% and a market return of 10%, what is the alpha for the following funds?

Manager Average Annual Return Beta

Manager D 11% 0.90

Manager E 15% 1.10

Manager F 15% 1.20

First, we calculate the portfolio's expected return:

ER(D)= .05 + 0.90 (.10-.05) = .0950 or 9.5% return

ER(E)= .05 + 1.10 (.10-.05) = .1050 or 10.50% return

ER(F)= .05 + 1.20 (.10-.05) = .1100 or 11% return

Then, we calculate the portfolio's alpha by subtracting the expected return of the portfolio from the actual return:

Alpha D = 11%- 9.5% = 1.5%

Alpha E = 15%- 10.5% = 4.5%

Alpha F = 15%- 11% = 4.0%

Which manager did best? Manager E did best because, although manager F had the same annual return, it was expected that manager E would yield a lower return because the portfolio's beta was significantly lower than that of portfolio F.

Of course, both rate of return and risk for securities (or portfolios) will vary by time period. The Jensen measure requires the use of a different risk-free rate of return for each time interval considered. So, let's say you wanted to evaluate the performance of a fund manager for a five-year period using annual intervals; you would have to also examine the fund's annual returns minus the risk-free return for each year and relate it to the annual return on the market portfolio, minus the same risk-free rate.

Conversely, the Treynor and Sharpe ratios examine average returns for the total period under consideration for all variables in the formula (the portfolio, market and risk-free asset). Like the Treynor measure, however, Jensen's alpha calculates risk premiums in terms of beta (systematic, undiversifiable risk) and therefore assumes the portfolio is already adequately diversified. As a result, this ratio is best applied to something like a mutual fund.

**Common Hedge Fund Strategies**

Hedge fund strategies encompass a broad range of risk tolerance and investment philosophies within a wide array of investments, including debt and equity securities, commodities, currencies, derivatives, real estate and other investment vehicles. The horizon of hedge fund investment strategies has seen unprecedented expansion in recent years. Below is a description of some of the more common hedge fund strategies. Note that hedge fund investment terms are driven in large part by the fund’s strategy and its level of liquidity. See our article: Brief Survey of Common Hedge Fund Terms.

**Long/Short Equity**

One of the most commonly used strategies for startup hedge funds is the long/short equity strategy. As the name suggests, the long/short equity strategy involves taking long and short positions in equity and equity derivative securities. Funds using a long/short strategy employ a wide range of fundamental and quantitative techniques to make investment decisions. Long/short funds tend to invest primarily in publicly traded equity and their derivatives, and tend to be long biased. Long/short funds also tend to have fairly straightforward investment fund terms. Accordingly, lock-ups, gates and other withdrawal terms in long-short funds are usually on the more permissive side because of the ease of liquidating positions when needed to facilitate investor withdrawals.

**Credit Funds**

Credit funds make debt investments based on lending inefficiencies. Credit funds tend to follow cyclical patterns, and are most active following economic downturns and restrictions in the credit market. Credit funds include distressed debt strategies, fixed income strategies, direct lending and others.

**Distressed Debt**

Distressed debt involves investment in corporate bonds, bank debt, and occasionally common and preferred stock of companies in distress. When a company is unable to meet its financial obligations, or is in a liquidity crisis, its debt is devalued. Distressed debt funds use fundamental analysis to identify undervalued investments. Hedge funds that invest in distressed debt need to employ more stringent lock-up and withdrawal terms, including side pockets, (accounts to separate illiquid assets). A fund sponsor looking to form a distressed debt fund should speak with experienced legal counsel to determine whether a private equity fund would be more appropriate. Unlike hedge funds, that allow regular withdrawals, private equity funds are usually closed-ended and have a finite duration, typically between five and ten years.

**Fixed Income**

Fixed income funds invest in long-term government, bank and corporate bonds, debentures, convertible notes, capital notes, and their derivatives, which pay a fixed rate of interest. Many fixed income funds have lower risk tolerances than distressed debt funds and place capital preservation as a higher priority, leading to more diversification and volatility-reducing strategies. A common fixed income hedge fund strategy is fixed income arbitrage, discussed below.

**Arbitrage**

Arbitrage strategies seek to exploit observable price differences between closely-related investments by simultaneously purchasing and selling investments. When properly used, arbitrage strategies produce consistent returns with low risk. However, because price inefficiencies between investments tend to be slight, arbitrage funds must rely heavily on leverage to obtain significant returns. Due to heavy use of leverage, some arbitrage firms have suffered monumental losses when pricing differences unexpectedly shifted (including Long Term Capital Management, the infamous fixed income arbitrage fund from the 1990s that suffered catastrophic losses and had to be bailed out by a government-brokered consortium of Wall Street banks).

**Fixed Income Arbitrage**

Fixed income arbitrage seeks to exploit pricing differences in fixed income securities, most commonly by taking various opposing positions in inefficiently priced bonds or their derivatives, with the expectation that prices will revert to their true value over time. Common fixed income arbitrage strategies include swap-spread arbitrage, yield curve arbitrage and capital structure arbitrage.

**Convertible Arbitrage**

Convertible arbitrage seeks to profit from price inefficiencies of a company’s convertible securities relative to its company’s stock. At its most basic level, convertible arbitrage involves taking long positions in a company’s convertible securities while simultaneously taking a short position in a company’s common stock. Although simple in theory, proper execution of convertible arbitrage strategies requires careful timing to avoid losses. Furthermore, the increasing popularity of convertible arbitrage has had the effect of diminishing available price inefficiencies, making it difficult to achieve significant returns without using extensive leverage.

**Relative Value Arbitrage**

Relative value arbitrage, or “pairs trading” involves taking advantage of perceived price discrepancies between highly correlated investments, including stocks, options, commodities, and currencies. A pure relative value arbitrage strategy involves high risk and requires extensive expertise.

**Merger Arbitrage**

Merger Arbitrage involves taking opposing positions in two merging companies to take advantage of the price inefficiencies that occur before and after a merger. Upon the announcement of a merger, the stock price of the target company typically rises and the stock price of the acquiring company typically falls. Merger arbitrage is a form of event-driven hedge fund strategy, discussed below.

**Event Driven**

Event-driven strategies are closely related to arbitrage strategies, seeking to exploit pricing inflation and deflation that occurs in response to specific corporate events, including mergers and takeovers, reorganizations, restructuring, asset sales, spin-offs, liquidations, bankruptcy and other events creating inefficient stock pricing. Event-driven strategies require expertise in fundamental modeling and analysis of corporate events. Examples of event-driven strategies include: merger arbitrage, risk arbitrage, distressed debt, and event-based capital structure arbitrage.

**Quantitative (Black Box)**

Quantitative hedge fund strategies rely on quantitative analysis to make investment decisions. Such hedge fund strategies typically utilize technology-based algorithmic modeling to achieve desired investment objectives. Quantitative strategies are often referred to as “black box” funds, since investors usually have limited access to investment strategy specifics. Funds that rely on quantitative technologies take extensive precautions to protect proprietary programs.

**Global Macro**

Global macro refers to the general investment strategy making investment decisions based on broad political and economic outlooks of various countries. Global macro strategy involves both directional analysis, which seeks to predict the rise or decline of a country’s economy, as well as relative analysis, evaluating economic trends relative to each other.

Global macro funds are not confined to any specific investment vehicle or asset class, and can include investment in equity, debt, commodities, futures, currencies, real estate and other assets in various countries. Currency traders rely heavily on global macro strategies to forecast relative currency values. Likewise, interest rate portfolio managers, which trade instruments that are keyed into sovereign debt interest rates, are heavily involved with global macro fundamental analysis.

**Multi-Strategy**

Multi-strategy funds are not confided to a single investment strategy or objective, but use a variety of investment strategies to achieve positive returns regardless of overall market performance. Multi-strategy funds tend to have a low risk tolerance and maintain a high priority on capital preservation. Even though multi-strategy funds have the discretion to use a variety of strategies, we have found that fund managers tend to focus primarily on one or more core investment strategies.