In the preceding section, we saw that the application of modern portfolio
theory results in a higher expected return for a given level of risk or, alternatively,
less risk for a given level of expected return.
This is clearly an attractive proposition to investors in credit assets.
However, there are some challenges that we face in applying modern portfolio
theory—something that was developed for equities—to credit assets.
Credit Assets Do Not Have Normally Distributed
Loss Distributions
Modern portfolio theory is based on two critical assumptions. The first assumption
is that investors are “risk averse.” Risk aversion just means that


if the investor is offered two baskets of assets—basket A and basket B—
where both baskets have the same expected return but basket A had higher
risk than basket B, the investor will pick basket B, the basket with the
lower risk. And that assumption is not troublesome. It is likely that investors
in credit assets are at least as risk averse as equity investors.
The second assumption—the troublesome one—is that security returns
are jointly normally distributed. This means that the expected return and
standard deviation completely describe the return distribution of each security.
Moreover, this assumption means that if we combine securities into
portfolios, the portfolio returns are normally distributed.
First, we have to do some mental switching of dimensions. For equities,
we are interested in returns. For loans and other credit assets, we are
interested in expected losses. So the question becomes: Can the loss distributions
for loans and other credit assets be characterized as normal
distributions? And, as long as we are here, we might as well look at the
distribution of equity returns.
Exhibit 2.5 examines these questions. Panel A of Exhibit 2.5 contains
a normal distribution and the histogram that results from actual daily price
change data for IBM. It turns out that the daily price changes for IBM are
not normally distributed: There is more probability at the mean than
would be the case for a normal distribution; and there are more observations
in the tails of the histogram than would be predicted by a normal distribution.
(The actual distribution has “fat tails.”) Indeed, if you look at
equities, their returns are not, in general, normally distributed. The returns
for most equities don’t pass the test of being normally distributed.
But wait a minute. We said that a critical assumption behind modern
portfolio theory is that returns are normally distributed; and now we have
said that the returns to equities are not normally distributed. That seems to
be a problem. But in the case of equity portfolios, we simply ignore the deviation
from normality and go on. In just a moment, we examine why this
is okay for equities (but not for credit assets).
Panel B of Exhibit 2.5 contains a stylized loss distribution for an “originate-
and-hold” portfolio of loans. Clearly, the losses are not normally distributed.
Can we just ignore the deviation from normality as we do for equity
portfolios? Unfortunately, we cannot and the reason is that credit portfolio
managers are concerned with a different part of the distribution than are
the equity managers.
Managers of equity portfolios are looking at areas around the mean.
And it turns out that the errors you make by ignoring the deviations from
normality are not very large. In contrast, managers of credit portfolios focus
on areas in the tail of the distribution. And out in the tail, very small
errors in the specification of the distribution will have a very large impact.
Modern Portfolio Theory and Elements of the Portfolio Modeling Process 35
EXHIBIT 2.5