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REV: FEBRUARY 20, 2007
ANDRÉ F. PEROLD
Introduction to Portfolio Theory
op yo Portfolio theory is concerned with the risk-reducing role played by individual assets in an investment portfolio of several assets. The benefits of diversification were first formalized in 1952 by
Harry Markowitz, who later was awarded the Nobel Prize in economics for this work. Portfolio theory is today a cornerstone of modern financial theory, as well as a widely used tool for managing risk-return tradeoffs in investment portfolios. This note examines the basic building blocks of the theory. Means and Standard Deviations of Total Return
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Figure 1
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The return and risk of an asset are commonly…show more content… The formula for the standard deviation (SP) of a portfolio of cash and asset B is:
SP = fSB
tC
i.e., if we invest all our money in B(f = 1) then SP = SB; if we invest half of our money in B and half in cash, then our risk is only half as large (SP = ½SB); and so on.
Both EP and SP are thus linearly related to the means and standard deviations of the assets in the portfolio. This is always true for EP but only sometimes true for SP, here because SA = 0. Graphically, these relationships are as follows:
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Figure 3
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Introduction to Portfolio Theory
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Each point on the line in Figure 3 (say, the line through A and B) is the mean-standard deviation pair corresponding to a particular combination of A and B. For example, the point halfway between
A and B gives the mean and standard deviation of a portfolio that is 50% invested in A and 50% invested in B. The lines extend beyond B and C by taking f to be larger than 1. This is possible if we can borrow at the rate of return on A (EA) and leverage our investment in B or C.
Problems
Would you rather hold portfolios of A and B or A and C?
2.
Whichever line (A-B or A-C) you choose to be on, how will you decide where to be on the line, i.e., what fraction