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# ## The Risk Assessment Spectrum: A Critical Tool for Investors Pt2

Thu, 20 Dec 2012 10:53:07 GMT

The ‘basic bucket’ explained

Let’s focus on the ‘basic bucket’ and look at each individual measurement.

When we are talking about deviation type statistics, a common one is Standard Deviation.  Basically, you are measuring the variation of your returns around a mean – how spread out are your returns? Do they tend to be around the mean? Or are they all over the place or piled on either end of the spectrum?  The problem with this is that if you try to use it as a risk statistic, you have to have some standard deviation to make money and you can’t just judge an investment based on say, a higher standard deviation.  It’s tough to find an investment which makes 2% a month, every month, which would result in a zero standard deviation.  You are more likely to find an investment which has periods of positive or negative returns, thus to get the returns you are looking for, you have standard deviation to get the results which are not always based around the mean.  Your mean is not always sitting at 2% every month.  Therefore, standard deviation is needed to make money but we also have to consider the downside deviation: What does our investment look like when we lose?  Instead of measuring the returns around the mean, we want to measure the losses and how far away the returns are from zero.  This gives us a more accurate understanding of how bad it really is when you lose.

Alpha and Beta are regular terms which come to mind when discussing portfolio risk.  One thing that investors often mistake is that alpha is not a subtraction, it does not mean take a return and subtract a benchmark return from It, thus the difference equating to the alpha.  The alpha is really the result of a regression, you regress the benchmark returns against the investment returns and then you determine how much added value you get by investing in that particular instrument. It’s a measure of added value on top of the benchmark.  Beta on the other hand is a measure from that same regression; you are basically saying take this cloud of points and fit a line to those points.  The beta shows how well that line fits.  How close was the investment to the actual returns of the benchmark?  It’s an indicator of both direction and strength of the movement when compared to the market.

Correlation is another term that investors seem pretty familiar with – the vale range from negative one to one.  If you have a correlation of one, you are the same as the benchmark.  However, if you have a correlation of negative one, you are opposite to the benchmark.  When your benchmark is up by 5%, you are down 5%.  If you have a correlation of zero, that shows that the investment lacks a relationship with the benchmark and no matter how the benchmark does, it doesn’t have an effect on how the investment acts or operates. So, correlations are often thought of as a way to measure how diversified we are.  If the correlations are low, then we seem to think that’s a diversified portfolio.  There are ways to do variations of correlations.  A classic correlation would take all the data points that you have and then compute a correlation against that and see how things operate.  Alternatively, you can remove your outliers and then carry out your calculations. Remember, outliers are rare events, things that don’t happen that often so they can sometimes swing the numbers.

Let’s move onto another familiar term and that’s Risk Adjusted Return; an evaluation of the investment, taking risk into account.  A typical way to think about it would be to take the return of your investment and subtract whatever you think your risk free rate of return is (good luck finding a risk free rate of return one in today’s world!).  The idea is that we need to establish whether you are generating more of a return than the amount of risk that I am taking after I remove that part of the return that I could get just lying around.  Sharpe ratio does that by defining risk as standard deviation.  Another to consider would be Sortino ratio, here instead of standard deviation as your risk, use downside deviation

Omega on the other hand is a newer statistic which tries to give you some risk-adjusted return.  It’s really measuring the number of returns you have above whatever you think your minimum acceptable rate of return is which is what MAR stands for.  When thinking about a risk free rate of return (which could be zero or 1%), you want to know how many returns you have above whatever my acceptable rate is, taking into account standard deviation, Skewness and Kurtosis, and thus defining more moments in our distribution.  Just a couple of things to note here regarding risk-adjusted return; we have to have the same risk free rate in order to be able to compare.  If you are calculating a Sharpe ratio at 1% but another individual uses 1%, then the numbers are meaningless.  Therefore, if you see a label that says Sharpe or Sortino and it doesn’t tell you what the risk free rate is, there is no use for that statistic because they can’t be compared utilizing juxtaposition.

Distribution statistics are widely used when analyzing your portfolio risk.  We often hear terms such as Skewness and Kurtosis.  But what do they really mean?  Skewness is a measure of the shape of your bell curve.  It would be the point of that distribution skewed left or right; it is not classically around the mean but more in one direction or the other.  It characterizes the degree of asymmetry of a distribution around its mean.  By using skewness, investors should be able to better predict whether a return is likely to be positive or negative. Kurtosis is the measure of how tall a distribution is.  Is it flat? Are we getting a lot of variation and replication of those variants in the distribution? Are all of the returns around the center point of the mean? If this were the case, the distribution would be very high. Kurtosis characterizes the relative peakedness or flatness of a distribution, helping investors better predict the likelihood of a given return or loss. VaR (Value at Risk) is a measure of confidence as to how much you would lose if you got into a losing situation.  Expected Tail Loss takes that a step further and analyzes the average loss past the VaR, so if your portfolio gets down to those areas of loss, you need to be able to predict what your worst case scenario would be.  It’s about predicting a ‘what if’ scenario.

Last but not least in our analysis of the ‘basic bucket’ we look at Monte Carlo Simulation.  In basic terms, Monte Carlo Simulation is derived from the concept of simulation by formulating a multitude of outcomes.  If we get enough outcomes, we ought to be able to find some probabilities around what might happen.  Investors use that as a way to forecast where to place your assets and put some probability around potential outcomes so that we get an idea of what might happen at a certain point in time.

We’ve looked at numerous risk analytics, all of which are cost effective ways to help you analyze what’s really going on inside your portfolio.  Check back with us soon for an analysis of our ‘intermediate bucket’ where we will focus on removing the normal distribution assumption and focus on factor and Fat-tailed analysis, risk budgeting and stress testing.

Check back soon for our analysis of the advanced bucket .