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Unformatted text preview: Fall 2010 Investment Management, FINE 441, Lecture Notes 34 1 Professor Ruslan Goyenko Asset Allocation across Risky and RiskFree Portfolios Fall 2010 Investment Management, FINE 441, Lecture Notes 34 2 Introduction Asset allocation decision refers to a choice among broad investment classes, such as stocks, longterm Tbonds, and short term Tbills. In this section, we shall study the most basic asset allocation choice: the choice of how to allocate ones investment fund between riskfree securities and risk asset classes. Fall 2010 Investment Management, FINE 441, Lecture Notes 34 3 Example 1 Suppose a portfolio of risky stocks P is your optimal risky portfolio (we shall discuss what it means to be optimal later). E(rp)=15%, and p=22%. The riskfree rate of return rf (Tbill rate) is 7%. You have $1,000 to invest and want 12% expected return for you investment. How should you combine the portfolio P and the riskfree asset? What is the standard deviation of the return on your investment? Fall 2010 Investment Management, FINE 441, Lecture Notes 34 4 Example 1 Contd Suppose you think the standard deviation of 13.75% is too risky, and want 10% standard deviation of return for your investment. What should be the allocation in this case? What is the expected return of this portfolio? Fall 2010 Investment Management, FINE 441, Lecture Notes 34 5 Capital Allocation Line (CAL) In addition to the two particular allocation choices above, we can examine the riskreturn combinations of all possible allocation choices. The cases where the weight on Tbill is negative are where you borrow at the riskfree rate and invest the borrowed amount in the risky portfolio P . Weight Weight Expected Standard Portfolio P TBill Return Deviation 1 0.07 0.1 0.9 0.078 0.022 0.2 0.8 0.086 0.044 0.3 0.7 0.094 0.066 0.4 0.6 0.102 0.088 0.5 0.5 0.11 0.11 0.6 0.4 0.118 0.132 0.7 0.3 0.126 0.154 0.8 0.2 0.134 0.176 0.9 0.1 0.142 0.198 1 0.15 0.22 1.10.1 0.158 0.242 1.20.2 0.166 0.264 1.30.3 0.174 0.286 1.40.4 0.182 0.308 Fall 2010 Investment Management, FINE 441, Lecture Notes 34 6 Capital Allocation Line Contd The Capital Allocation Line (CAL) is simply a plot of these combinations in a meanstandard deviation space: CAL depicts the riskreturn combinations available by varying asset allocation between a riskfree asset and a risky portfolio. 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Standard deviation Expected return Capital Allocation Line Fall 2010 Investment Management, FINE 441, Lecture Notes 34 7 Sharpe Ratio The slope of the CAL, called the Sharpe ratio (or rewardtorisk ratio), equals the increase in expected return that can be obtained per unit of additional standard deviation. It is a measure of the riskreturn tradeoff (extra return per extra risk), and is give by Thus, the Sharpe ratio is a ratio of risk premium to standard deviation....
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 Spring '08
 RUSLANGOYENKO

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