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Traffic is moderately heavy and the lights are poorly timed. the true path and Random 1), the Ulcer Index shows a sharp contrast between the strategies.įor a more concrete way of picturing the Ulcer Index, imagine driving a car along a 55 mph speed limit road with stoplights spaced every half mile. Even in cases where the maximum drawdown is similar (e.g. Only the Ulcer Index can fully differentiate among these paths. The metrics for each path are shown in the table below: Along with the true realized path, I have included the path with the returns reversed and five paths with random permutations of the true returns. Using the Ulcer Index, we can finally distinguish between strategies that have the same annualized return, annualized volatility, and maximum drawdown: Strategies B and C have Ulcer Indices of 11.2% and 12.8%, respectively.Īs a case study, the following chart shows the return of a 60/40 portfolio of SPY and AGG rebalanced at the beginning of each year from 01/2004 to 12/2013. Whereas, the maximum drawdown is only the largest Ri, which can only increase through time, the Ulcer Index encapsulates every drawdown into one summary statistic that adapts to new data as it is realized. Where N is the total number of data points and each Ri is the fractional retracement from the highest price seen thus far. It is calculated using the following formula: It not only factors in the severity of the drawdowns but also their duration. In fact, Strategies B and C shown previously have the same maximum drawdown of 25%.Įnter the Ulcer Index. Still, maximum drawdown lacks information about the length of the drawdown, which can have a substantial impact on investors’ perception of a strategy. Maximum drawdown does this by measuring the worst loss from peak to trough over the time period. To differentiate between these two strategies using summaries statistics, we must capture the sequence of the returns.
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To illustrate this concept, the following simulated paths both have the same realized volatility. This also applies to the Sharpe and Sortino ratios. However, annualized volatility only depends on what returns were realized, not in what order they came. It is a quantity that is likely to change if your “route” changes. We could call volatility a path dependent metric, much like mechanical work is in thermodynamics. Therefore, we look at metrics like annualized volatility, which incorporates the individual realized returns over a time period. If it were as simple as that, the two strategies shown below would be equivalent, but even a novice investor would likely choose to have owned strategy A.
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This is somewhat similar to a state variable in physics, such as temperature change, entropy, and internal energy, which depends only on the initial and final states. Much like average speed simply uses the total time and distance traveled, annualized return smooths over any intermediate details. To calculate this, all we need is the starting and ending point what happened in between is irrelevant. In finance, one typical summary statistic is the annualized return of a strategy. These classifications add context to what is being described based on how it is calculated and the information it contains. Many of the common metrics can be classified in ways that are similar to quantities we use to describe the world around us: temperature, speed, weight, voltage, etc. To use these statistics effectively, it is helpful to look at some of the nuances of those frequently cited and cases where the information they provide could be misleading. These numbers provide a summary of what happened to the strategy historically and can be useful to quickly compare different strategies. Investors utilize a variety of performance and risk metrics to evaluate strategies.