Lecture_03_04

Lecture_03_04 - Fall 2010 Investment Management, FINE 441,...

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Unformatted text preview: Fall 2010 Investment Management, FINE 441, Lecture Notes 3-4 1 Professor Ruslan Goyenko Asset Allocation across Risky and Risk-Free Portfolios Fall 2010 Investment Management, FINE 441, Lecture Notes 3-4 2 Introduction Asset allocation decision refers to a choice among broad investment classes, such as stocks, long-term T-bonds, and short- term T-bills. In this section, we shall study the most basic asset allocation choice: the choice of how to allocate ones investment fund between risk-free securities and risk asset classes. Fall 2010 Investment Management, FINE 441, Lecture Notes 3-4 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 risk-free rate of return rf (T-bill 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 risk-free asset? What is the standard deviation of the return on your investment? Fall 2010 Investment Management, FINE 441, Lecture Notes 3-4 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 3-4 5 Capital Allocation Line (CAL) In addition to the two particular allocation choices above, we can examine the risk-return combinations of all possible allocation choices. The cases where the weight on T-bill is negative are where you borrow at the risk-free rate and invest the borrowed amount in the risky portfolio P . Weight Weight Expected Standard Portfolio P T-Bill 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 1.1-0.1 0.158 0.242 1.2-0.2 0.166 0.264 1.3-0.3 0.174 0.286 1.4-0.4 0.182 0.308 Fall 2010 Investment Management, FINE 441, Lecture Notes 3-4 6 Capital Allocation Line Contd The Capital Allocation Line (CAL) is simply a plot of these combinations in a mean-standard deviation space: CAL depicts the risk-return combinations available by varying asset allocation between a risk-free 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 3-4 7 Sharpe Ratio The slope of the CAL, called the Sharpe ratio (or reward-to-risk ratio), equals the increase in expected return that can be obtained per unit of additional standard deviation. It is a measure of the risk-return trade-off (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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Lecture_03_04 - Fall 2010 Investment Management, FINE 441,...

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