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The Forex Portfolio Theory

A somewhat different approach to risk measurement is provided by portfolio theory. Portfolio
theory starts from the premise that investors choose between portfolios on the basis of their
expected return, on the one hand, and the standard deviation (or variance) of their return, on
the other.6 The standard deviation of the portfolio return can be regarded as a measure of the
portfolio’s risk. Other things being equal, an investor wants a portfolio whose return has a high
expected value and a low standard deviation. These objectives imply that the investor should
choose a portfolio that maximises expected return for any given portfolio standard deviation.
A portfolio that meets these conditions is efficient, and a rational investor will always choose
an efficient portfolio. When faced with an investment decision, the investor must therefore
determine the set of efficient portfolios and rule out the rest. Some efficient portfolios will
have more risk than others, but the more risky ones will also have higher expected returns.
Faced with the set of efficient portfolios, the investor chooses one particular portfolio on the
basis of his or her own preferred trade-off between risk and expected return. An investor who
is very averse to risk will choose a safe portfolio with a low standard deviation and a low
expected return, and an investor who is less risk averse will choose a riskier portfolio with a
higher expected return.
One of the key insights of portfolio theory is that the risk of any individual asset is not the
standard deviation of the return to that asset, but the extent to which that asset contributes to
overall portfolio risk. An asset might be very risky (i.e., have a high standard deviation) when
considered on its own, and yet have a return that correlates with the returns to other assets in
our portfolio in such a way that acquiring the new asset does not increase the overall portfolio
standard deviation. Acquiring the new asset would then be riskless, even though the asset held
on its own would still be risky. The moral of the story is that the extent to which a new asset
contributes to portfolio risk depends on the correlation or covariance of its return with the
returns to the other assets in our portfolio - or, if one prefers, the beta, which is equal to the
covariance between the return to asset i and the return to the portfolio divided by the variance
of the portfolio return. The lower the correlation, other things being equal, the less the asset
contributes to overall risk. Indeed, if the correlation is negative, it will offset existing risks and
lower the portfolio standard deviation.
Portfolio theory provides a useful framework for handling multiple risks taking account
of how those risks interact with each other. It is therefore of obvious use to - and is widely
used by - portfolio managers, mutual fund managers and other investors. However, it tends to
run into estimation and data problems. The risk-free return is not too difficult to estimate, but
estimating the expected market return and the betas is often problematic. The expected market
return is highly subjective and each beta is specific not only to the individual asset to which
it refers, but also to our current portfolio. To estimate a beta coefficient accurately, we need
data on the returns to the new asset and the returns to all our existing assets, and we need a
sufficiently long data set to make our statistical estimation techniques reliable. The beta also
depends on our existing portfolio and we should, in theory, re-estimate all our betas every time
our portfolio changes.
For some time after it was first advanced in the 1950s, the data and calculation requirements
of portfolio theory led many to see it as quite impractical. To get around some of these problems.

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