Measuring And Managing Investment Risk
Investopedia | Saturday, 27 August 2011
We tend to think of "risk" in predominantly negative terms, as something to be avoided or a
threat that we hope won't materialize. In the investment world, however, risk is inseparable
from performance and, rather than being desirable or undesirable, is simply necessary.
Understanding risk is one of the most important parts of a financial education. This article
will examine ways that we measure and manage risk in making investment decisions.
Risk - Good, Bad and Necessary
A common definition for investment risk is deviation from an expected outcome. We can express
this in absolute terms or relative to something else like a market benchmark. That deviation
can be positive or negative, and relates to the idea of "no pain, no gain" - to achieve higher
returns in the long run you have to accept more short-term volatility. How much volatility
depends on your risk tolerance - an expression of the capacity to assume volatility based on
specific financial circumstances and the propensity to do so, taking into account your
psychological comfort with uncertainty and the possibility of incurring large short-term
losses.
Absolute Measures of Risk
One of the most commonly used absolute risk metrics is standard deviation, a statistical
measure of dispersion around a central tendency. For example, during a 15-year period from
August 1, 1992, to July 31, 2007, the average annualized total return of the S&P 500 Stock
Index was 10.7%. This number tells you what happened for the whole period, but it doesn't
say what happened along the way.
The average standard deviation of the S&P 500 for that same period was 13.5%. Statistical
theory tells us that in normal distributions (the familiar bell-shaped curve) any given
outcome should fall within one standard deviation of the mean about 67% of the time and
within two standard deviations about 95% of the time. Thus, an S&P 500 investor could
expect the return at any given point during this time to be 10.7% +/- 13.5% just under 70%
of the time and +/- 27.0% 95% of the time.
Risk and Psychology
While that information may be helpful, it does not fully address an investor's risk concerns.
The field of behavioral finance has contributed an important element to the risk equation,
demonstrating asymmetry between how people view gains and losses. In the language
of prospect theory, an area of behavioral finance introduced by Amos Tversky and Daniel
Kahneman in 1979, investors exhibit loss aversion - they put more weight on the pain
associated with a loss than the good feeling associated with a gain.
Thus, what investors really want to know is not just how much an asset deviates from its
expected outcome, but how bad things look way down on the left-hand tail of
the distribution curve. Value at risk (VAR) attempts to provide an answer to this question.
The idea behind VAR is to quantify how bad a loss on an investment could be with a given
level of confidence over a defined period of time. For example, the following statement
would be an example of VAR: "With about a 95% level of confidence, the most you stand to
lose on this $1,000 investment over a two-year time horizon is $200." The confidence level is
a probability statement based on the statistical characteristics of the investment and the
shape of its distribution curve.
Of course, even a measure like VAR doesn't guarantee that things won't be worse.
Spectacular debacles like hedge fund Long Term Capital Management in 1998 remind us that
so-called "outlier events" may occur. After all, 95% confidence allows that 5% of the time
results may be much worse than what VAR calculates. In the case of LTCM, the outlier
event was the Russian government's default on its outstanding sovereign debt obligations, an
event that caused the hedge fund's performance to be much worse than its expected value at
risk.
Another risk measure oriented to behavioral tendencies is drawdown, which refers to any
period during which an asset's return is negative relative to a previous high mark. In
measuring drawdown, we attempt to address three things: the magnitude of each negative
period (how bad), the duration of each (how long) and the frequency (how many times).
Risk: The Passive and the Active
In addition to wanting to know, for example, whether a mutual fund beat the S&P 500 we
also want to know how comparatively risky it was. One measure for this is beta, based on
the statistical property of covariance and also called "market risk", "systematic risk", or "nondiversifiable risk". A beta greater than 1 indicates more risk than the market and vice versa.
Beta helps us to understand the concepts of passive and active risk. The graph below shows
a time series of returns (each data point labeled "+") for a particular portfolio R(p) versus
the market return R(m). The returns are cash-adjusted, so the point at which the x and y axes
intersect is the cash-equivalent return. Drawing a line of best fit through the data points
allows us to quantify the passive, or beta, risk and the active risk, which we refer to as alpha.
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The gradient of the line is its beta. For example, a gradient of 1.0 indicates that for every unit
increase of market return, the portfolio return also increases by one unit. A manager
employing a passive management strategy can attempt to increase the portfolio return by
taking on more market risk (i.e. a beta greater than 1) or alternatively decrease portfolio risk
(and return) by reducing the portfolio beta below 1.
Influence of Other Factors
If the level of market or systematic risk were the only influencing factor, then a portfolio's
return would always be equal to the beta-adjusted market return. Of course, this is not the
case - returns vary as a result of a number of factors unrelated to market risk. Investment
managers who follow an active strategy take on other risks to achieve excess returns over the
market's performance. Active strategies include stock, sector or country selection,
fundamental analysis and charting.
Active managers are on the hunt for alpha - the measure of excess return. In our diagram
example above, alpha is the amount of portfolio return not explained by beta, represented as
the distance between the intersection of the x and y axes and the y axis intercept, which can
be positive or negative. In their quest for excess returns, active managers expose investors to
alpha risk - the risk that their bets will prove negative rather than positive. For example, a
manager may think that the energy sector will outperform the S&P 500 and increase her
portfolio's weighting in this sector. If unexpected economic developments cause energy
stocks to sharply decline, the manager will likely underperform the benchmark - an example
of alpha risk.
A note of caution is in order when analyzing the significance of alpha and beta. There must
be some evidence of a linear pattern between the portfolio returns and those of the market,
or a reasonably inclusive line of best fit. If the data points are randomly dispersed, then the
line of best fit will have little predictive ability and the results for alpha and beta will be
statistically insignificant. A general rule is that an r-squared of 0.70 or higher (1.0 being
perfect correlation) between the portfolio and the market reasonably validates the
significance of alpha, beta and other relative measures.
The Price of Risk
There are economic consequences to the decision between passive and active risk. In
general, the more active the investment strategy (the more alpha a fund manager seeks to
generate) the more an investor will need to pay for exposure to that strategy. It helps to
think in terms of a spectrum from a purely passive approach. For example, a buy and hold
investment into a proxy for the S&P 500 - all the way to a highly active approach such as a
hedge fund employing complex trading strategies involving high capital commitments and
transaction costs. For a purely passive vehicle like an index fund or an exchange trade fund
ETF) you might pay 15-20 basis points in annual management fees, while for a high-octane
hedge fund you would need to shell out 200 basis points in annual fees plus give 20% of the
profits back to the manager. In between these two extremes lie alternative approaches
combining active and passive risk management.
The difference in pricing between passive and active strategies (or beta risk and alpha risk
respectively) encourages many investors to try and separate these risks: i.e. to pay lower fees
for the beta risk assumed and concentrate their more expensive exposures to specifically
defined alpha opportunities. This is popularly known as portable alpha, the idea that the
alpha component of a total return is separate from the beta component.
For example a fund manager may claim to have an active sector rotation strategy for beating
the S&P 500 and show as evidence a track record of beating the index by 1.5% on an
average annualized basis. To the investor, that 1.5% of excess return is the manager's value the alpha - and the investor is willing to pay higher fees to obtain it. The rest of the total
return, what the S&P 500 itself earned, arguably has nothing to do with the manager's unique
ability, so why pay the same fee? Portable alpha strategies use derivatives and other tools to
refine the means by which they obtain and pay for the alpha and beta components of their
exposure.
Conclusions
Risk is inseparable from return. Every investment involves some degree of risk, which can
be very close to zero in the case of a U.S. Treasury security or very high for something such
as concentrated exposure to Sri Lankan equities or real estate in Argentina. Risk is
quantifiable both in absolute and in relative terms. A solid understanding of risk in its
different forms can help investors to better understand the opportunities, trade-offs and
costs involved with different investment approaches.
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