Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Expected Rate of Return -  Example: Risk & Return

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Risk in Real Estate Investing  Risk Defined  Intuitively –  Mathematically –  Graphically –

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Measuring Risk: Variance  Variance is  Example:

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Measuring Risk: Standard Deviation  Standard Deviation is  Example:

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Coefficient of Variation is  Example: Coefficient of Variation

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Diversification  Stand Alone Risk vs. Portfolio Risk  Diversification

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Expected Rate of Return on a Portfolio of Assets -  Example: Portfolio Returns

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Portfolio Risk  The standard deviation of a portfolio is  Example #1: Perfect Negative Correlation  

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Portfolio Risk, cont.  Example #2: Perfect Positive Correlation   Example #3: Partially Correlated Assets 

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Standard Deviation of A Portfolio  Generic Case:  2 Asset portfolio:

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Example #1: Consider an investor with a 2 asset portfolio. Thirty Percent of the investor’s portfolio is invested in common stocks with an expected return of 12.5%, while the remaining seventy percent of the portfolio in invested in corporate bonds which offer an expected return of 8.5%. The standard deviation of return for the two individual investments are 25% and 10% respectively. If the correlation coefficient between the two asset’s returns is 0.60, what is the expected return, and standard deviation of expected return for this portfolio? Std. Dev. of A Portfolio, cont.

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  3 Asset Portfolios:  Variance/Covariance Matrix: Std. Dev. of A Portfolio, cont.

Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Example #2: Consider an investor with a 3 asset portfolio. Thirty Percent of the investor’s portfolio is invested in common stock with an expected return of 15%, an additional thirty percent of the investor’s portfolio is invested in corporate bonds with an expected return of 12%, while the remaining forty percent of the portfolio in invested in real estate which offers an expected return of 11%. The standard deviation of return for the three individual investments are 18%, 16%, and 14% respectively. If the correlation coefficient between the stock and bond returns is 0.50, the correlation coefficient between the bond and real estate returns is 0.65, and the correlation coefficient between the stock and real estate returns is 0.70, what is the expected return, and standard deviation of expected return for this portfolio? Std. Dev. of A Portfolio, cont.