RedGage

The primary purpose of risk measurement is to help identify the source of
risk, quantify the risk, and then control the risk within a given
portfolio.



Modern portfolio theory teaches us that the risk in a portfolio is
derived from the volatility in the price of the asset (i.e. how much the
price jumps up and down from day to day). The best explanation is how
Benjamin Graham described what causes market price movements:

"In the short run, the market is like a voting machine--tallying up
which firms are popular and unpopular. But in the long run, the market
is like a weighing machine--assessing the substance of a company."



To help us uncover why our portfolio moves up and down in value, we need
the help of a conceptual framework called the Risk Triangle. The Risk
Triangle decomposes the major components of risk measurement into -
Factor Analysis, Value at Risk (VAR) and Stress Testing. We will use
this framework throughout the remaining of this post to hang together
the notion of risk in a cohesive way.



Sourcing Risk:



Modern portfolio theory tells us that you are only compensated for the
risks you take (i.e. there is no such thing as a free lunch). Because of
that fact, the returns both positive and negative are derived from what
is known as factors.



Factors can really be anything you want them to be, such as meaningful
factors like oil, large cap growth or nonsensical factors like the
number of times a cat crosses the road and the number of times a cricket
chirps within a two minute span.



An example should help crystallize the concept. Take for example an oil
company and its relationship to the price of oil. If the price of oil
goes up, then the company makes more profit and is therefore worth more
(and the inverse is true). The former relationship is obvious, but what
about a not-so-obvious example with a diaper manufacturer and how it
relates to the price of oil. Unless you know a lot about diaper
manufacturing you probably wouldn’t know that petroleum is a major cost
input into the process to manufacture diapers. So if the price of oil
goes up, then the costs of diaper manufacturing go up, then profits fall
and therefore the company is worth less (and the inverse is true).



Most relationships in economics are not straightforward and are very
complex. Being able to tease apart those factors and relationships is
difficult at best and impossible at worst. In any case, it isn’t
something you can do in your mind once the number of factors exceeds
one. This difficulty can be overcome with a little statistical
gymnastics known as factor analysis.



There are two forms of factor analysis - multi-linear regression and
principle component analysis (PCA). The best way to think of them is
bottom up and top down. With multi-linear regression the user would
identify the factors and put them into the risk measurement software.
The system would tell you how good of a job you did describing the risk
in the portfolio. The problem here is that if you put garbage in, then
you get garbage out. Alternatively with PCA it is more of a top down
approach. The risk measurement software will tell you how much of the
risk can be explained. Only then do you enter the factors you are
interested in and the system will tell you much each factor actually
explains the risk (a.k.a. risk decomposition).



That all may seem overwhelming, but don’t worry about it. The main fact
is that there is software that will take care of it for you and it
implements both methodologies. This is a good thing because having both
approaches helps you compare and contrast against each other. For
instance, if the multi-linear regression approach says you didn’t do a
good job explaining the risk then you may thing that there isn’t a way
to explain the risk. Otherwise having the PCA approach along side the
multi-linear regression approach we can determine that the overall risk
can be explained very well. Thus we must not have done a very good job
at picking our factors and must return to the drawing board.



It is also important to note at this time the type of risk we have been
implicitly talking about is called market risk. There are actually four
components to market risk - equity risk, interest rate risk, currency
risk and commodity risk. Equity risk is due to the fluctuations of stock
prices. Interest rate risk is due to changes in prices due to
fluctuations in the interest rate (e.g. when interest rates rise, bond
prices fall). Currency risk is due to the fluctuations in exchange rates
that can cause a gain/loss in the asset. Commodity risk is due to the
changes in commodity prices like the one mentioned above (e.g. oil, gold
and copper).



We will review some examples of these risks a bit later in our next
posting and also cover quantifying risk with VAR and Stress Tests.