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Portfolio analysis

Portfolio analysis. Management 4430.02 Class notes by A.P. Palasvirta. Geometric average return. Annualized return if you know the purchase price and the sale price of an asset. Forecasting risk & return. Expected return Standard deviation Covariance. Historical risk & return.

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Portfolio analysis

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  1. Portfolio analysis Management 4430.02 Class notes by A.P. Palasvirta

  2. Geometric average return 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. Annualized return if you know the purchase price and the sale price of an asset

  3. Forecasting risk & return 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Expected return • Standard deviation • Covariance

  4. Historical risk & return 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. Mean return Standard deviation Covariance

  5. Contrasting methods 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Forecasting • Forward looking • Must determine possible outcomes • Probabilities of those outcomes • Completely speculative • Historical • Backward looking • Using time series data • Completely definitive • Statistics derived mean exactly the same thing

  6. Covariance/variance matrix 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  7. Correlation 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Correlation normalizes covariance • value of +1 means perfect positive correlation • value of 0 means independence between data series • value of -1 means perfect negative correlation

  8. Diversification 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Correlation is a measure of how two assets react together to economic market conditions • High positive correlation • Two assets are affected similarly by economic events • High negative correlation • Two assets are affected in completely opposite ways by economic events • Independence -zero correlation • Two assets are act independent of each other relative to economic events

  9. Portfolio Statistics Expected return to the portfolio of multiple assets Standard deviation to a portfolio of multiple assets 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  10. Two-asset Portfolio Preferred Portfolio Ep Efficient Set Opportunity Set Risk preferences SDP 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  11. Implications of Correlation Statistics 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • The lower the pair-wise correlation of two assets, the greater the diversification benefit of adding those assets to your portfolio • Adding assets which have low pair-wise correlation with each other to your portfolio reduces overall portfolio risk

  12. Affects of Correlation Ep High Correlation Low Correlation SDP 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  13. Three-asset Portfolio Ep SDP 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  14. Calculating Portfolio values - three asset portfolio 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  15. Multiple-asset Portfolio Ep SDP 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  16. Systematic Risk SDp SDM N 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  17. Systematic Risk 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • As you diversify your portfolio by adding assets, your portfolio standard deviation decreases • Optimal approx 20 assets = 21.68% • 20*100*$20 = $40,000 buying individual stocks • Buy funds which are already diversified • When you are fully diversified, your risk is the risk of the market portfolio • By changing portfolio proportions you can modify risk to suit your preferences

  18. Optimal Portfolio U2 U1 Capital Market Line EM More risk averse Less risk averse SDM 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  19. Any efficient portfolio will be found on the capital market line Capital market line 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  20. Capital Asset Pricing Model 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Prices the risk of asset relative to its systematic risk • gives the required rate of return relative to its systematic risk • Risk-free rate of return • Beta • Risk premium

  21. The Risk-free Asset 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • The risk-free asset does not exist except as a theoretical concept • assets used t-bills or t-bonds • Low default risk - government backing • For calculation of the company β, companies often use the t-bond rate that has a similar term

  22. Beta 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. β measures only the systematic risk of an assets β is also a covariance that is normalized by something, the variance of the market β measures the risk of holding that firms stock in a fully diversified portfolio

  23. Risk premium 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D. • Return to the market portfolio less the return to the risk-free rate of return • Return to the market portfolio • Uses the 90 day return to the a broad based stock index • Toronto stock exchange index • Dow index • S&P 500 index • T-bond rate of appropriate term

  24. Statistics 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  25. Security Market Line RM β = 1 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  26. Security Market Line - Change in rate of inflation RM RM Inflation adjustment β = 1 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

  27. Security Market Line -Change in Risk Premium RM RM Slope change reflecting increased Systematic Risk β = 1 4430.02 Portfolio analysis Notes: A.P. Palasvirta, Ph.D.

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