II: Portfolio Theory I 2: Measuring Portfolio Return 3: Measuring Portfolio Risk 4: Diversification

Chapter 2: Measuring Portfolio Return Return & Risk © Oltheten & Waspi 2012 Markets are efficient only if return exactly compensates for risk

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Measuring Portfolio Return  Holding Period Return  Cash Flow Adjusted Rate of Return  Time Weighted versus Statistical Rates of Return  Internal Rate of Return

Chapter 2: Measuring Portfolio Return Holding Period Return $2,400,000 = $1.20 = $1 + 20% $2,000,000 $1,600,000 = $0.80 = $1 - 20% $2,000,000 For every $ you started with you now have $1.20 $ you started with + 20% For every $ you started with you now have only $0.80 $ you started with - 20%

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Holding Period Return  When you use the alternate formula you are subtracting out the $ you started with at the very beginning $2,400,000 - $2,000,000 = 1.20 –1 =.20 = +20% $2,000,000 $$ you started with $ you started with

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Cash Flow Adjusted Rate of Return  We want to measure investment returns  We adjust so that the rate of return is not distorted by cash flows over which the investment manager has no control.

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Cash Flow Adjusted Rate of Return  Each Investment Manger began the month of September with $1million. At the end of the month  Alice: $1m to $1.56 million  Bob: $1m to $1.54 million  Carol: $1m to $1.50 million

Chapter 2: Measuring Portfolio Return Cash Flow Un-adjusted Slope of 50% © Oltheten & Waspi 2012

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Cash Flow Adjusted  Each investment manager received an additional $300,000 from the client during the month  Alice: before the open on the first  Bob: on the tenth  Carol: after the close on the thirtieth Cannot measure as a rate of return any money that the investment manager did not generate.

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Cash Flow Adjusted Rate of Return  Alice:  Bob:  Carol:

Chapter 2: Measuring Portfolio Return Cash Flow Adjusted Slope of 20% not 50% © Oltheten & Waspi 2012

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Cash Flow Adjusted December 31Market Value:$34,978, January 3:Bond Income:$14, January 15:Pension contribution:$3, January 18:Bond Income:$ January 21:Pension Payments- $9, January 22:Dividend received$1, January 31:Pension contribution$3, January 31Market Value$34,993,897.09

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Time-Weighted verses Statistical  Time Weighted: combines time periods using Geometric totals and averages  Statistical: combines time periods using arithmetic totals and averages

Chapter 2: Measuring Portfolio Return Time-Weighted verses Statistical January February March April May June - 50% +50% -50% +50% -50% +50% Six month return = ? © Oltheten & Waspi 2012

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Statistical  Total Return =  Average Return =  Variance =  Standard Deviation =

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Statistical  Statistical returns assume that the return in one month is independent of the returns of any other month. February April June January March May - 50% + 50% $1,000,000

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Time-Weighted  Total Return =  Average Return =

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Time-Weighted  Time Weighted returns assume that returns in one month are reinvested in the following month $421,875 $1,000,000 $500,000 $281,250 $750,000 $375,000 $562,500 January February March April May June %

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Time-Weighted = Holding Period  In the absence of excluded cash flows, time weighted returns equal holding period returns. $421,875 $1,000,000 $500,000 $281,250 $750,000 $375,000 $562,500 January February March April May June %

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 Internal Rate of Return  Internal rate of return (IRR) is the rate of return that renders the Net Present Value (NPV) equal to zero.

Chapter 2: Measuring Portfolio Return Internal Rate of Return Dec 31, 2012 Dec 31, 2013 Dec 31, 2014 Dec 31, 2015 Dec 31, $10,000 +$510 +$2,000 +$4,500 +5,000 © Oltheten & Waspi 2012 IRR = 6%

Chapter 2: Measuring Portfolio Return © Oltheten & Waspi 2012 In Summary: Measuring Return  Holding Period Rate of Return  Cash Flow Adjusted Rate of Return  Time Weighted vs Statistical Rates of Return  Internal Rate of Return

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Measuring Risk  Risk versus Uncertainty  Standard Deviation (  )  Coefficient of Variation (CV)  Beta (β)

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Risk vs Uncertainty  In this example there is risk but no uncertainty

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Risk vs Uncertainty  Stock returns are normally distributed (more or less) so there is risk, but there is still uncertainty… 5 sigma event r~ N(0, 1)

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012  In the normal distribution 99.74% of the observations are within 3 standard deviations of the mean. Standard Deviation

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Standard Deviation  Easy to visualize Probability of making a loss

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Coefficient of Variation  Risk per unit of Return  CV = σ. E[R]

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Coefficient of Variation  Is the added return worth the added risk?

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Beta  Captures Market Risk  (Market Model) We will generate the market model through our discussion of diversification

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 In Summary: Measuring Risk  Risk versus Uncertainty  Standard Deviation  Coefficient of Variation  Beta

Chapter 3: Measuring Portfolio Risk © Oltheten & Waspi 2012 Risk Preferences  Risk Averse  Investors accept risk only if they are compensated  Risk Neutral  Investors are blind to risk and simply choose the highest expected return  Risk Loving  Investors actually derive utility from risky behavior (like gambles)

Chapter 4: Diversification © Oltheten & Waspi 2012 Diversification  Diversification reduces risk exposure when returns are imperfectly correlated.  Covariance & Correlation (review)

Chapter 4: Diversification © Oltheten & Waspi 2012 Covariance  Expectations vs Actual Stocks:  =11%,  = Bonds:  =7%,  =8.1650

Chapter 4: Diversification © Oltheten & Waspi 2012 Covariance  Deviations for the expected value Stocks:  =11%,  = Bonds:  =7%,  =8.1650

Chapter 4: Diversification © Oltheten & Waspi 2012 Covariance  Variance = average squared deviation:  Covariance = average product of the deviations: StocksBondsCombined Squared Deviation DevDeviation 2 DevDeviation 2 17%289-10%10017% * -10% = -170% 1%10%01% * 0% = 0% -18%32410%100-18% * 10% = -180%  =  2 = Covariance =  =

Chapter 4: Diversification © Oltheten & Waspi 2012 Correlation  = Covariance (Stocks, Bonds)  (Stocks)  (Bonds)  = =  = 0 Ocean Waves  = +1 Scaffold  = -1 Teeter-Totter

Chapter 4: Diversification © Oltheten & Waspi 2012 Portfolio Risk & Return  Portfolio Return  weighted average return of components  = w1 r1 + w2 r2  Portfolio Variance  Weighted variance of components adjusted for the correlation coefficient  = w12  (w1  1  1,2w2  2) + w22  22

Chapter 4: Diversification © Oltheten & Waspi 2012 Portfolio Risk & Return: an example  A portfolio of two stocks  Tardis Intertemporal  E[r] = 15%  = 20%  Hypothetical Resources  E[r] = 21%  = 40%  r = 0.30

Chapter 4: Diversification © Oltheten & Waspi 2012 Efficient Portfolio Frontier

Chapter 4: Diversification Efficient Portfolio Frontier (  =0.3) © Oltheten & Waspi 2012

Chapter 4: Diversification Efficient Portfolio Frontier © Oltheten & Waspi 2012

Chapter 4: Diversification Efficient Portfolio Frontier (  =0.3) r f = 10% © Oltheten & Waspi 2012

Chapter 4: Diversification © Oltheten & Waspi 2012 Limits of Diversification  Unsystematic Risk  Industry or firm specific – can be diversified away  Systematic Risk  Economy wide - cannot be diversified away

II: Portfolio Theory I