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Class Business

Class Business. Upcoming Groupwork Fund Clip #1 Fund Clip #2. Quiz. A client asks your advice about her investments. She has invested $50,000 in a Mosaic mutual fund and $30,000 in risk-free bonds. She asks you whether she should re-allocate her assets.

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Class Business

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  1. Class Business • Upcoming Groupwork • Fund Clip #1 • Fund Clip #2

  2. Quiz • A client asks your advice about her investments. She has invested $50,000 in a Mosaic mutual fund and $30,000 in risk-free bonds. She asks you whether she should re-allocate her assets. • You are analyzing the returns of the Mosaic fund and compare them with the S&P 500 ETF. You expect the Mosaic fund to have an expected return of 10% and a standard deviation of 25%. The S&P 500 ETF has an expected return of 8% and a standard deviation of 16%. The risk-free rate is currently 3%.

  3. Quiz • Question 1: What is the expected return and the standard deviation of her current portfolio? • The expected return is: E(r)=0.625(0.10) + 0.375(0.03) = 7.4% • The standard deviation is: Stdev(r)=0.625*0.25 = 15.62%

  4. Quiz • Question 2: Assume that she can borrow and lend at an interest rate of 3%. • Find a portfolio that dominates her current portfolio (same total risk but higher expected return)?

  5. Quiz • Find reward to variability ratios: • RTV Mosaic= • RTV S&P 500 = • So S&P 500 ETF has a higher-sloped CAL. • It is nearer to the “tangency” portfolio than Mosaic

  6. Quiz

  7. Quiz • Equation for S&P 500 CAL: • Your friend’s current portfolio has a standard deviation of .1562 and an expected return of 7.4%. • By dumping Mosaic and investing in the S&P 500 ETF she could have an expected return of

  8. Quiz • Figure out the dollar amount required. • To find the dollar amounts invested in each security, first find fraction of investment equity needed in each asset: w = 0.98 (1-w) = .02 • The total equity = $80,000, • Invest 2% of equity in risk-free asset ($1600) • Invest 98% of equity ($78,400) in the S&P 500 ETF. • If we knew the covariation between the Mosaic Fund and the S&P ETF, we could possibly find an even better combination including all three!

  9. Portfolio Allocation Example 2 1

  10. Portfolio Allocation Example • Suppose tangency portfolio is • Risky Asset 1: 60% • Risky Asset 2: 40% • Suppose you have $100 and only want • $50 in tangency portfolio • $50 in risk-free asset • Then you would have • __________ in asset 1 • __________ in asset 2 • __________ in risk-free asset $30 or 30% $20 or 20% $50 or 50%

  11. Portfolio Allocation Example • Suppose tangency portfolio is • Asset 1: 60% • Asset 2: 40% • Suppose you want • 125% of investment equity in tangency portfolio • -25% in risk-free asset • What fraction of funds would you put in each asset? Asset 1: 75% Asset 2: 50% Risk free: -25%

  12. Portfolio Allocation • What about the case of many risky assets? • The efficient frontier has the same shape • Intuition is the same Tangency Portfolio Expected Return Individual Assets Best possible CAL risk free rate Standard Deviation

  13. Portfolio Allocation • How to solve for Tangency Portfolio? • Easy to solve for using a computer • Spreadsheets are a little more awkward, but it can be done. • Upcoming Homework

  14. Portfolio Allocation • Three steps to determine the optimal portfolio: (A short version of steps given in example.) • 1) Compute and draw the efficient frontier • 2) Incorporate the risk free asset to find the best possible CAL • 3) Choose where you want to be on the CAL by borrowing or lending at the risk-free rate. • Money managers solve (1) and (2) • Inputs = estimates of E[rp] and Stdev[rp] • Better inputs, better results you earn more $$. • Individuals determine (3)

  15. Diversification and Many Risky Assets • Two risky assets • Recall example when r = -1 • We were able to eliminate all risk • When -1 < r <1 • we were able to eliminate some risk

  16. Diversification and Many Risky Assets • What if we create portfolios of many risky assets? • Decomposing realized returns: • E[rit]= mi • rit= mi + biMt + eit • Mt = random variable (mean 0) • Macro-wide shock • et= random variable (mean 0) • Firm-specific shock unique to each firm • The actual, realized return is the sum of • What we expect • Macro Shock • Firm-Specific Shock

  17. Diversification and Many Risky Assets • Consider an equally weighted portfolio of these returns. • Suppose we have n assets in portfolio • Weight in each asset is 1/n As n gets large The variance of e does not matter.

  18. Diversification • In general, as the number of assets increases in a portfolio, firm-specific shocks are washed out. What happens if there are no macro-shocks? Unsystematic risk n

  19. Diversification and Many Risky Assets • Since returns can be written as • The variance of the return is Systematic Risk Unsystematic Risk

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