PK AirFinance
What is Financial Risk?
by Nils Hallerström (
[email protected]) PK AirFinance – www.pkair.com Updated 2000-05-15
returns, are what we try to shun away from, the intuitively most appealing risk measure would be some kind of shortfall risk measure. This can be calculated by taking the probability weighted average of all outcomes below a certain threshold. This threshold could be the expected return, the risk-free rate of return, zero, or some kind of market benchmark return.
Risk is fashionable. But what is it? Traditionally, ex ante financial risk has been expressed as the standard deviation of the assumed return distribution from a financial investment. The more dispersed the possible outcomes are, the more risk the investor takes. This definition has a drawback. Suppose the upside potential is capped. That will reduce the standard deviation. But does it make the investment less risky? Intuitively, it is not so much the dispersion of returns that bother an investor, but losses or returns below ones expectations.
5.50% 5.00% 4.50%
Probability
4.00%
5.50%
3.50%
Expected Return
5.00% 3.00%
4.50%
Average Downside Risk
Standard Deviation
4.00% 3.50% 3.00%
2.50% 2.00% 1.50%
2.50%
Expected Return 2.00%
1.00%
1.50%
0.50%
1.00% 0.00%
0.50% -40%
0.00% -30% -20% -10% 0%
-40%
10%
20%
30%
40%
50%
60%
70%
-30%
-20%
-10%
0%
10%
20%
30%
Return
80%
Return
Return distribution for an asymmetrical investment – i.e. a loan
Return distribution for a symmetrical investment
In SAFE, we have chosen zero return as the benchmark and called this Average Downside Risk (ADR). Mathematically, ADR can be expressed as
If an investment proposition has a symmetrical return expectation – above expected returns and below expected returns are symmetrically distributed between the expected return – then standard deviation would make sense. However, in many investments there is an asymmetrical return distribution. This is the case with loans, where the upside is capped at the contractual margin and the fees. The downside is unlimited. The distribution has a “fat tail”. Most investments display some degree of asymmetry. Whilst standard deviation may be fine for investment propositions with Normal (Gauss, Bell Curve) probability distributions, it is inappropriate as a risk measure for most real life situations.
0
ADR= ∫ R × F(R) dR –∞
where R is the return and F(R) is the probability density function.
The full risk picture in an investment, or a portfolio of investments, is given by – a picture! This is the Return – Probability distribution. Returns are plotted on the x-axis and the associated probability is plotted on the y-axis.
Another purpose is to make sure you are able to withstand adverse events and avoid bankruptcy by being adequately capitalized. In this case, we are more interested in the bad case scenario.
The problem with pictures is that they cannot be ranked for selecting investments. They are two-dimensional and rankings are made along one dimension. Therefore, we have to define appropriate risk measures for our purpose.
A helpful risk measure in this case would be to look at the largest negative return which will not be exceeded with a certain confidence. Such measures are called Value at Risk (VaR). VaR assumes a certain confidence level. 99% or 99.5% or 95%. It also assumes a certain time horizon. Daily, weekly, yearly or for the horizon of your portfolio. The confidence level is chosen based on how badly you want to avoid bankruptcy. A 99% level means that statistic ally, you would go bankrupt once
One purpose is to evaluate transactions from a risk-reward point of view. For this, it would be appropriate to use some kind of average risk measure. Since losses, or below expected
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PK AirFinance
ment amount at a 90% confidence level, it would also be true for the 99% confidence level!
every 100 years. That would put your company or portfolio at a BB rating. The time horizon depends on how liquid your investments are. In SAFE, we use the tenor of the deal as the horizon since aircraft backed loans are somewhat illiquid.
It should be noted that risk measured on individual investments cannot be added on a portfolio level. Correlations between the performance of the individual investments have to be taken into account when constructing the return-probability graph for the portfolio.
On an individual investment level, VaR can be problematic. Very risky investments could have a probability of a total loss in excess of your confidence interval. If VaR equals the full invest-
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