Lab Report of Portfolio Valuation
NEKN82 EMPIRICAL FINANCE
LAB 3 Report
Done by:
Lang, Qin 1988-12-05
Low Lihui Valerie 1989-09-24
Q1
Before we evaluate the actual investment performance of the five constructed portfolios for period 1992.02-2008.07, we firstly calculate the mean, variance and standard deviation of each of the portfolio using Excel. The results are generated as below: Portfolios | Z1 | Z2 | Z3 | Z4 | Z5 | Zm | Mean | 0.008490 | 0.003843 | 0.009980 | 0.000141 | 0.004840 | 0.0066 | Variance | 0.005335 | 0.007238 | 0.004951 | 0.008652 | 0.00491 | 0.003932 | Standard Deviation | 0.073039 | 0.085075 | 0.070361 | 0.093016 | 0.070071 | 0.062707 |
Sharpe Ratio
According to Keith Cuthbertson and Dirk Nitzsche (2004), Sharp ratio measures the slope of the transformation line that, through constructing the tangency portfolio we can find the optimum weight to invest in risky assets. It is defined for any portfolio i as: sri = ERi -Rfσi where E[Ri] is the expected return on portfolio i, σi denotes the variance of portfolio i, and
Rf is the risk-free rate. To estimate the Sharpe ratio based on one period returns, we have sri= Mean (Zit)Std (Zit)
For aggregation over time, the Sharpe ratio for q period returns is q times the Sharpe ratio computed above, if serially uncorrelated returns exist. Therefore, we have sri (q) = q sri
The corresponding results generated by Excel are presented as follows, Portfolios | Z1 | Z2 | Z3 | Z4 | Z5 | Sharp ratio | 0.116237 | 0.045171 | 0.14184 | 0.001515 | 0.069077 | Sharp ratio (yearly) | 0.402655 | 0.156477 | 0.49135 | 0.005247 | 0.239288 |
Next, we perform a significance test for the estimated Sharpe ratios. Assume that returns are IID. The hypotheses for the test statistic are:
H0: sri = 0
H1: sri ≠ 0 (sri < 0 or sri > 0)
The test statistic is then defined as sri ~ N(0, 1+12sri2T)
Assume 5% significance level, we calculate the P-value in Excel for each portfolio using
LAB 3 Report
Done by:
Lang, Qin 1988-12-05
Low Lihui Valerie 1989-09-24
Q1
Before we evaluate the actual investment performance of the five constructed portfolios for period 1992.02-2008.07, we firstly calculate the mean, variance and standard deviation of each of the portfolio using Excel. The results are generated as below: Portfolios | Z1 | Z2 | Z3 | Z4 | Z5 | Zm | Mean | 0.008490 | 0.003843 | 0.009980 | 0.000141 | 0.004840 | 0.0066 | Variance | 0.005335 | 0.007238 | 0.004951 | 0.008652 | 0.00491 | 0.003932 | Standard Deviation | 0.073039 | 0.085075 | 0.070361 | 0.093016 | 0.070071 | 0.062707 |
Sharpe Ratio
According to Keith Cuthbertson and Dirk Nitzsche (2004), Sharp ratio measures the slope of the transformation line that, through constructing the tangency portfolio we can find the optimum weight to invest in risky assets. It is defined for any portfolio i as: sri = ERi -Rfσi where E[Ri] is the expected return on portfolio i, σi denotes the variance of portfolio i, and
Rf is the risk-free rate. To estimate the Sharpe ratio based on one period returns, we have sri= Mean (Zit)Std (Zit)
For aggregation over time, the Sharpe ratio for q period returns is q times the Sharpe ratio computed above, if serially uncorrelated returns exist. Therefore, we have sri (q) = q sri
The corresponding results generated by Excel are presented as follows, Portfolios | Z1 | Z2 | Z3 | Z4 | Z5 | Sharp ratio | 0.116237 | 0.045171 | 0.14184 | 0.001515 | 0.069077 | Sharp ratio (yearly) | 0.402655 | 0.156477 | 0.49135 | 0.005247 | 0.239288 |
Next, we perform a significance test for the estimated Sharpe ratios. Assume that returns are IID. The hypotheses for the test statistic are:
H0: sri = 0
H1: sri ≠ 0 (sri < 0 or sri > 0)
The test statistic is then defined as sri ~ N(0, 1+12sri2T)
Assume 5% significance level, we calculate the P-value in Excel for each portfolio using
Bibliography: Keith Cuthbertson, Dirk Nitzsche, 2004, Quantitative Financial Economics, second edition, John Wiley & Sons Ltd, England, pp. 170-174 Thomas H. Goodwin, 1998, The Information Ratio, Financial Analysts Journal, Vol. 54, No. 4 B.P.S. Murthi Yoon K. Choi, Preyas Desai, 1997, Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach, European Journal of Operational Research 98, pp. 408-418 David A. Sauer, 1997, The impact of social-responsibility screens on investment performance: Evidence from the Domini 400 social index and Domini Equity Mutual Fund, Review of Financial Economics, Volume 6, Issue 2, pp. 137-149