Class Note 6_S2010

# Class Note 6_S2010 - RSM 330 Investments Class 6 Maureen...

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RSM 330 – Investments Class 6 – July 22, 2010 Maureen Stapleton, CFA 1 RSM 330 - note 6_S2010

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Plan for Today Short Project Proposal is due today Mid Term Exam July 27 at 6 pm in WO35 (optional) Sample exams and an exam checklist are posted Email me if you have a conflict Practical Asset Allocation Commodities Policy portfolios / Benchmark Portfolios Investment Horizons Mean reversion Readings for Today: Bodie textbook 6 th edition: 22.1 – 22.2 and pg. 804; 23.1 – 23.2 A note on Exchange Rate Risk Whatever happened to the Balanced Portfolio? 2 RSM 330 - note 6_S2010
Practical Asset Allocation Problem How to allocate money among T-bills, bonds, and stocks ? In this example, we use real returns (ie after inflation) Step One: Forecast the required parameters (9 parameters) 1 . Expected returns for each of the three assets, 2. Variances for each of the three assets 3. Three covariances: Cov(T-bills, bonds), Cov(T-bills, stocks), and Cov(bonds, stocks). How do we estimate these parameters? 3 RSM 330 - note 6_S2010

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Let’s use the historical average of annual real returns :   Expected Returns : Expected Real Return T-Bills 0.5% Bonds 2.0% Stocks 6.8% Variances and Covariances T-Bills 4.0% 1.00 0.60 0.10 Bonds 10.5% 0.60 1.00 0.21 Stocks 21.0% 0.10 0.21 1.00 Correlations Asset Standard Deviation T-Bills Bonds Stocks 4 RSM 330 - note 6_S2010
Step Two: Find the investment opportunity set. We know from last week (Class Note 5) that the investment opportunity set will be an area , because we have more than two risky assets. The portfolio weights are w 1 for T-Bills, w 2 for bonds, and w 3 for stocks. We want to see the range of possible values of E and S as we vary w i : E = w 1 E(r TB ) + w 2 E(r B ) + w 3 E(r S ) Var = w 2 1 Var(r TB ) + w 2 2 Var(r B ) + w 2 3 Var(r S ) +2w 1 w 2 Cov(r TB , r B ) + 2w 1 w 3 Cov(r TB , r S ) +2w 2 w 3 Cov(r B , r S ) Portfolio weights must always sum to one: w 1 + w 2 + w 3 = 1. 5 RSM 330 - note 6_S2010

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First, impose a constraint on leverage: No buying on margin or short selling 0   w 1 , w 2 , w 3 1 . Three points on the efficient frontier 6 RSM 330 - note 6_S2010
Use an optimization algorithm, to find w 1 , w 2 , w 3 such that To minimize Var(w 1 r TB + w 2 r B + w 3 r S ) Subject to E (w 1 r TB + w 2 r B + w 3 r S ) = E and w 1 + w 2 + w 3 = 1 The restrictions imposed are: w 1 0, w 2 0, w 3 0. Three portfolios are on the efficient frontier: Portfolio Expected Standard T-Bills Bonds Stocks Return Deviation w 1 w 2 w 3 A 2% 6.1% 70% 8% 22% B 4% 11.5% 17% 36% 47% C 6% 18.0% 6% 16% 78% Remember that these are real (after inflation) returns – that’s why they look low! 7

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## This note was uploaded on 07/16/2011 for the course COMMERCE 330 taught by Professor Stapleton during the Fall '10 term at University of Toronto.

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Class Note 6_S2010 - RSM 330 Investments Class 6 Maureen...

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