Ratio Definitions
Alpha – Alpha is a measure of a fund’s performance by comparison to its benchmark. It represents the return of the fund when the benchmark is assumed to have a return of zero and indicates the extra value a manager’s activities have contributed: if the Alpha is 5, the fund has outperformed its benchmark by 5%. A further aspect of Alpha emerges when it is taken in conjunction with Beta. If a strong R-Squared correlation exists, the Beta will show how volatile the fund is compared to its benchmark and indicate how much extra risk the manager has taken on in order to get that high-Alpha performance. So, Alpha indicates better/worse performance compared with the index, whilst Beta shows higher/lower risk.
Beta – Beta is the estimate of a fund’s volatility by comparison to its benchmark, i.e. how sensitive the fund is to movements in the section of the market that comprises the benchmark. A fund with a Beta close to 1 means that the fund will generally move in line with the benchmark. Higher than 1 and the fund is more volatile than the benchmark, so that with a Beta of 1.5, say, the fund will be expected to rise or fall 1.5 points for every 1 point of benchmark movement. It’s important to stress that Beta is just an estimate: however, the stronger the R-Squared correlation between fund and benchmark, the more reliable this estimate becomes.
Downside Capture Ratio – shows the fund’s performance in a down market relative to the benchmark. A Downside Capture Ratio that is less than 100% demonstrates that when the market went down the fund caught only a fraction of the losses, and the lower the down capture the better. E.g. If a fund has a Downside Capture Ratio of 85% this tells us that the fund captured only 85% of the benchmark’s negative performance during a down market. The ratio is calculated by taking the funds downside capture returns and dividing it by the benchmark’s downside capture returns over the same time period.
Downside Risk – Downside risk is a measurement that considers only negative returns. It is calculated as a downside deviation of returns below a specified risk-free rate. It represents an estimation of a security’s potential to suffer a decline in price in negative market conditions and could be considered as an estimate of the potential loss on any investment.
Information Ratio – So called because it assesses the degree to which a manager uses skill and knowledge to enhance returns, this is a versatile and useful risk-adjusted measure of actively managed fund performance. It is calculated by deducting the returns of the fund’s benchmark from the fund’s overall returns, then dividing the result by its Tracking Error (which is a measure of the volatility of those excess returns). In this way, we arrive at the value, per unit of extra risk assumed, that the manager’s decisions have added to what the market would have delivered anyway. The higher the Information Ratio the better. As ever, the R-squared between the fund and its benchmark must be strong if any discrete reliance is to be placed on the Information Ratio.
Jensens alpha – This is a risk-adjusted measure used to gauge the extent to which a manager has added value to the returns that could have been expected from a benchmark portfolio, while taking into account the fund’s sensitivity to that benchmark.
The starting value uses the benchmark’s average return in excess of a notional risk-free rate. The riskfree rate is the rate that could have been earned from investments generally considered “safe,” such as gilts or cash equivalents. The benchmark’s average return over the risk-free rate is then adjusted by multiplying it by the beta of the fund. This adjustment compensates for the fund’s sensitivity (or lack of it) to the movements in the market.
The result produced is the expected rate. This is the rate that could be expected from the fund’s return in the given market with the same degree of sensitivity to that market, where there is no active intervention from the portfolio manager.
Jensen’s alpha is therefore:
(fund return/risk-free rate ) – expected rate
Jensen’s alpha is therefore a test of whether the fund has achieved better performance than the beta would suggest. If the value is positive, it indicates an active management style with superior stockpicking ability. If the value is negative, it indicates that returns are falling short of the adjusted benchmark return.
It can be useful to investors seeking funds with low sensitivity to the market — for example, to minimize downward movements in bear conditions. If two funds have similar lower betas, then the one with the better positive Jensen’s alpha is making superior returns for the same reduced level of downside risk.
Finally, since Jensen’s alpha is calculated by reference to a fund’s beta, a strong r-squared correlation between the fund and its benchmark is important if the measure is to have any significance.
Maximum Drawdown – Represents the worst possible return over a period, e.g. buying at the maximum price over the period and selling at the worst.
Max loss – This represents the worst running return over a period — for example, the longest running consecutive loss without making a gain.
r2 – The r-squared measure is an indication of how closely correlated a fund is to an index or a benchmark. It can be treated as a percentage, showing the proportion of a fund’s movements that can be attributed to those of the benchmark. Values for an r-squared measurement range between 0 and 1, with 0 indicating no correlation at all and 1, rarely, showing a perfect match. Values upward of 0.7 suggest that the fund’s behavior is increasingly closely linked to its benchmark, whereas the relevance diminishes as the r-squared measurement descends toward 0.5 and starts to disappear altogether below 0.5. 15 R-squared is a key ratio, in that other measures of a fund’s performance — such as alpha and beta — will have been calculated by reference to its benchmark. The weaker the r-squared correlation, the more unsuitable the benchmark is and the more unreliable these measures will be in assessing the fund.
Sharpe Ratio – This is a commonly used measure that calculates the level of a fund’s return over and above the return of a notional risk-free investment, such as cash or government bonds. The difference in returns is then divided by the fund’s standard deviation (volatility). The resulting ratio is an indication of the amount of excess return generated per unit of risk. In general, it is considered that the higher the Sharpe ratio, the better.
Sortino – This ratio is similar to the Sharpe ratio, using downside risk rather than standard deviation as the denominator. Thus, the Sortino ratio is calculated by subtracting the risk-free rate from the return of the portfolio and then dividing by the downside deviation. The Sortino ratio measures the return to “bad” volatility, thereby giving investors a measure to assess risk in a better manner than simply looking at excess returns to total volatility. A large Sortino ratio indicates a low risk.
Tracking error – This statistic measures the standard deviation of a fund’s excess returns over the returns of an index or benchmark portfolio. As such, it can be an indication of “riskiness” in the manager’s investment style. A tracking error below 2 suggests a passive approach, with a close fit between the fund and its benchmark. At 3 and above, the correlation is progressively looser and indicates that the manager will be deploying a more active investment style and taking bigger positions away from the composition of the benchmark.
While zero tracking error would indicate a fund that was a perfect replication of its benchmark portfolio, this is hardly likely to be encountered in reality. The fund will not be fully invested at all times in its benchmark components, since an element of liquidity will need to be retained for redemptions, and the assumed reinvestment of dividends will not always be possible. Transaction costs dilute returns — and proportionately more so in smaller funds. Issues of timing and availability mean that changes in the benchmark’s constituents cannot be instantaneously mirrored in the fund’s portfolio. These factors will all produce greater tracking error — and be reflected in the beta and r-squared ratios. Ultimately, this is actually only an “error” if the investment strategy goes unrewarded by outperformance of the benchmark.
Treynor – This is another risk-adjusted performance measure, similar in calculation and application to the Sharpe ratio. The difference is that while Sharpe weighs a fund’s returns against total risk (standard deviation, or volatility), Treynor looks at excess return for each unit of systemic risk (the volatility, inherent in the market that cannot be diversified).
The Treynor calculation takes the fund’s excess return over a notional risk-free rate, then divides it by the fund’s beta. A Treynor ratio greater than 1 shows that the fund has produced more units of return than of risk. Based on market risk alone, the ratio assumes that nonsystemic risk is capable of being eliminated by diversification across a wide range of investments, and it measures whether the systemic risk has been rewarded.
Also known as the volatility-to-reward ratio, Treynor is useful in comparing funds that invest in similar market sectors and achieve similar returns. For example, when assessing a range of UK equity funds, it is the one with the highest Treynor ratio that is taking on the least market risk to achieve its level of performance. Also, since it factors out the manager’s ability from movements in the fund’s sector, Treynor may be used to compare fund performances adjusted for systemic risks in different market sectors because, although intuitively the ratio should be higher for bond funds than for those investing entirely in equities, this is not necessarily true in every case. While not perfect, and not to be taken in isolation, the Treynor ratio can be a pointer to the optimum risk- and sector-adjusted fund for a particular risk-aversion profile.
Volatility – Standard deviation is a statistical measurement which, when applied to an investment fund, expresses its volatility, or risk. It shows how widely a range of returns varied from the fund’s average return over a particular period. Low volatility reduces the risk of buying into an investment in the upper range of its deviation cycle, then seeing its value head towards the lower extreme. For example, if a fund had an average return of 5%, and its volatility was 15, this would mean that the range of its returns over the period had swung between +20% and -10%. Another fund with the same average return and 5% volatility would return between 10% and nothing, but there would at least be no loss. While volatility is specific to a fund’s particular mix of investments, and comparison to other portfolios is difficult, clearly, for those that offer similar returns, the lower-volatility funds are preferable. There is no point in taking on higher risk than necessary in order to achieve the same reward.