FIN 604/730 — QUIZ 01 (Solutions)
1. Sharpe, Treynor, and Jensen Ratios
Given data:
Risk-free rate (Rf) = 7.5%
Market/Industry return (Rm) = 13.5%
PortfolioBetaSD (%)Return (%) M2.50119 N1.751412 Z4.001916
Formulas:
Sharpe = (Rp − Rf)/σ
Treynor = (Rp − Rf)/β
Jensen’s Alpha = Rp − [Rf + β(Rm − Rf)]
Portfolio
Sharpe
Treynor
Jensen’s Alpha
M
0.1364
0.0060
-13.50%
N
0.3214
0.0257
-6.00%
Z
0.4474
0.0213
-15.50%
Interpretation: Z has the highest Sharpe ratio, N performs best on Treynor ratio, but all have negative
Jensen’s alpha (underperforming CAPM).
2. Portfolio Risk and Return with Covariances
Given weights and returns:
Rp = Σ wiri = 0.45(0.10) + 0.30(0.18) + 0.25(0.13) = 13.15%
Covariances calculated using ρijσiσj
Cov(Alpha, Beta) = 0.013872
Cov(Beta, Gama) = 0.003553
Cov(Alpha, Gama) = -0.001188
Portfolio σ = √Var(Rp) = 10.14%
3. 3-day SMA and EMA
3-day Simple Moving Average (SMA): average of past 3 prices.
Exponential Moving Average (EMA): EMAt = αPt + (1−α)EMAt−1, α=2/(N+1)=0.5
Day
Closing
SMA(3)
EMA(3)
3
22
21.00
21.00
4
20.5
21.17
20.75
5
21.5
21.33
21.13
6
23
21.67
22.06
7
24
22.83
23.03
8
23
23.33
23.02
4. Fama’s Decomposition and Net Selectivity
CAPM expected return = Rf + β(Rm − Rf) = 0.07 + 1.52(0.16−0.07) = 20.68%
Jensen’s Alpha (Net Selectivity) = 0.17 − 0.2068 = −3.68%
Negative alpha ⇒ underperformed CAPM expectation.
Variance decomposition produced negative unsystematic variance (inconsistent data).
Final Summary
• Sharpe, Treynor, and Jensen ratios show relative performance among portfolios M, N, Z.
• Portfolio risk/return analysis shows diversification benefits (σ=10.14%).
• SMA and EMA calculations demonstrate trend smoothing techniques.
• Fama’s decomposition revealed data inconsistency but negative alpha (−3.68%) confirms
underperformance.