Can You Tell Which is Which ?

Can you tell which is Good, Bad or Ugly ?

A has the highest % of positive returns and the largest and longest DrawUp

But A has negative skewness and C has positive skewness

CBA

Why is C Good ?• C has positive skewness of +1.64

• C’s Maximum Drawdown was just -0.99% ten times lower than that of A’s (‘The Ugly”)

• The modified probability of C experiencing a negative return is only 23% versus A’s 35%

• C’s average returns when negative are 6 x less negative than those of A.

Why is B Bad ?• The main reason B is Bad is because it has zero

skewness and excess Kurtosis. While some might view this as a positive the problem is that this rarely occurs for real, thus potentially lulling people into a false sense of security where risk is either over or under-estimated.

• B does have the smoothest path as indicated by the K-Ratios which are a measure of smoothness.

• B also has the shortest Drawdown

Why is A Ugly ?• Despite having the highest proportion of positive

returns of 82%, A’s losses when they occur, happen together in clusters causing its average losses to be larger and its Maximum Drawdown to be ten times as high as C’s at -9.22%

• This is reflected best in A’s Gain-Loss and Omega Ratios but it scores the worst on almost all measures except of course for the Sharpe ( Normal ) Ratio which is unable to distinguish between the three.

Sharpe Ratio is unable to differentiate

These Can

Normal Assumption Misleads

ConclusionJust like in the Movie from which those three time series take their names, we are uncertain as to which one is the best. All of them end up in the same place but the one takes a less comfortable path than the others experiencing a -9.22% drawdown along the way. In the real world an investor into the ‘Bad’ asset may well have panicked and sold out. But when viewed using only the most widely used basic statistics and the assumption of Normality, we cannot differentiate between the three.

The point of the exercise is of course to make people aware of the importance of asymmetry in investments and of the relevance of the higher moments like skewness and excess Kurtosis in particular. In general it can be said that Investors have a preference for higher odd moments (1st moment = Mean, 3rd moment = Skewness) and lower even moments (2nd moment = Std Dev, 4th moment = Kurtosis ).

So the question you need to ask your investment provider is not whether or not they feel lucky, but whether or not they bother to measure their higher moment risks – most do not. As their clients you deserve to know if they do and if not why not. Next time you are viewing your funds factsheet see how many of these statistics you can find.

All of the statistics mentioned in this presentation and many more are available for all KiwiSaver Funds covered on the KnowRisk website www.knowrisk.biz

The Good

The Bad&

The Ugly……..Of Risk Statistics was brought to you by;

KnowRisk Consultingwe crunch the numbers so you don't have topeter.urbani@knowrisk.biz