(a)
To calculate:
We have to collect the data as given in Connect and calculate each fund's excess return.
Explanation of Solution
Excess returns are calculated as shown below. Period chosen is from 2004 to 2008.
|
|
Total monthly returns |
|
|
|
Excess Returns |
|
|
|
Month |
Vanguard |
Value Fund |
S&P |
T-bills |
Vanguard |
Value Fund |
S&P |
| Jan-04 | 1.52 | -0.07 | 1.35 | 0.07 | 1.45 | -0.14 | 1.28 |
| Feb-04 | -0.53 | -0.99 | -1.32 | 0.06 | -0.59 | -1.05 | -1.38 |
| Mar-04 | -2.69 | -2.46 | -1.89 | 0.09 | -2.78 | -2.55 | -1.98 |
| Apr-04 | 0.22 | 2.52 | 1.70 | 0.08 | 0.14 | 2.44 | 1.62 |
| May-04 | 2.53 | 1.39 | 1.85 | 0.06 | 2.47 | 1.33 | 1.79 |
| Jun-04 | -1.93 | -7.46 | -3.22 | 0.08 | -2.01 | -7.54 | -3.30 |
| Jul-04 | 0.99 | -0.78 | 0.25 | 0.1 | 0.89 | -0.88 | 0.15 |
| Aug-04 | 1.52 | 2.49 | 1.00 | 0.11 | 1.41 | 2.38 | 0.89 |
| Sep-04 | 0.21 | 1.46 | 1.29 | 0.11 | 0.10 | 1.35 | 1.18 |
| Oct-04 | 5.22 | 4.66 | 4.46 | 0.11 | 5.11 | 4.55 | 4.35 |
| Nov-04 | 3.24 | 3.60 | 3.01 | 0.15 | 3.09 | 3.45 | 2.86 |
| Dec-04 | -2.36 | -3.48 | -2.24 | 0.16 | -2.52 | -3.64 | -2.40 |
| Jan-05 | 3.62 | 0.79 | 2.09 | 0.16 | 3.46 | 0.63 | 1.93 |
| Feb-05 | -2.33 | -2.86 | -1.83 | 0.16 | -2.49 | -3.02 | -1.99 |
| Mar-05 | -2.68 | -2.41 | -1.87 | 0.21 | -2.89 | -2.62 | -2.08 |
| Apr-05 | 4.08 | 7.13 | 3.22 | 0.21 | 3.87 | 6.92 | 3.01 |
| May-05 | 2.25 | 0.51 | 0.15 | 0.24 | 2.01 | 0.27 | -0.09 |
| Jun-05 | 3.55 | 5.28 | 3.82 | 0.23 | 3.32 | 5.05 | 3.59 |
| Jul-05 | -1.85 | -0.85 | -0.93 | 0.24 | -2.09 | -1.09 | -1.17 |
| Aug-05 | 0.38 | 1.34 | 0.80 | 0.3 | 0.08 | 1.04 | 0.50 |
| Sep-05 | -1.88 | 0.30 | -2.36 | 0.29 | -2.17 | 0.01 | -2.65 |
| Oct-05 | 2.87 | 5.04 | 4.39 | 0.27 | 2.60 | 4.77 | 4.12 |
| Nov-05 | 0.93 | 0.46 | -0.19 | 0.31 | 0.62 | 0.15 | -0.50 |
| Dec-05 | 3.41 | 3.30 | 2.41 | 0.32 | 3.09 | 2.98 | 2.09 |
| Jan-06 | 0.00 | -1.82 | 0.57 | 0.35 | -0.35 | -2.17 | 0.22 |
| Feb-06 | 0.71 | 0.34 | 1.65 | 0.34 | 0.37 | 0.00 | 1.31 |
| Mar-06 | 0.53 | -0.45 | 1.26 | 0.37 | 0.16 | -0.82 | 0.89 |
| Apr-06 | -3.00 | -5.84 | -3.01 | 0.36 | -3.36 | -6.20 | -3.37 |
| May-06 | -0.27 | -1.55 | 0.26 | 0.43 | -0.70 | -1.98 | -0.17 |
| Jun-06 | 1.09 | -2.36 | 0.45 | 0.4 | 0.69 | -2.76 | 0.05 |
| Jul-06 | 2.70 | 3.60 | 2.18 | 0.4 | 2.30 | 3.20 | 1.78 |
| Aug-06 | 2.63 | 2.87 | 2.70 | 0.42 | 2.21 | 2.45 | 2.28 |
| Sep-06 | 2.56 | 1.92 | 3.16 | 0.41 | 2.15 | 1.51 | 2.75 |
| Oct-06 | 0.75 | 1.94 | 1.99 | 0.41 | 0.34 | 1.53 | 1.58 |
| Nov-06 | 2.32 | 0.22 | 0.77 | 0.42 | 1.90 | -0.20 | 0.35 |
| Dec-06 | 1.86 | 2.18 | 1.51 | 0.4 | 1.46 | 1.78 | 1.11 |
| Jan-07 | -2.30 | -1.69 | -1.96 | 0.44 | -2.74 | -2.13 | -2.40 |
| Feb-07 | 0.81 | 0.89 | 1.16 | 0.38 | 0.43 | 0.51 | 0.78 |
| Mar-07 | 3.87 | 2.92 | 4.42 | 0.43 | 3.44 | 2.49 | 3.99 |
| Apr-07 | 3.65 | 3.37 | 3.39 | 0.44 | 3.21 | 2.93 | 2.95 |
| May-07 | -2.02 | -1.14 | -1.46 | 0.41 | -2.43 | -1.55 | -1.87 |
| Jun-07 | -4.74 | -0.79 | -3.13 | 0.4 | -5.14 | -1.19 | -3.53 |
| Jul-07 | 1.12 | 1.11 | 1.28 | 0.4 | 0.72 | 0.71 | 0.88 |
| Aug-07 | 2.54 | 4.91 | 3.88 | 0.42 | 2.12 | 4.49 | 3.46 |
| Sep-07 | 0.39 | 2.19 | 1.35 | 0.32 | 0.07 | 1.87 | 1.03 |
| Oct-07 | -5.86 | -3.90 | -3.87 | 0.32 | -6.18 | -4.22 | -4.19 |
| Nov-07 | 0.25 | 0.00 | -1.13 | 0.34 | -0.09 | -0.34 | -1.47 |
| Dec-07 | -5.39 | -10.34 | -6.04 | 0.27 | -5.66 | -10.61 | -6.31 |
| Jan-08 | -2.67 | -2.38 | -2.58 | 0.21 | -2.88 | -2.59 | -2.79 |
| Feb-08 | -0.89 | -0.06 | -0.90 | 0.13 | -1.02 | -0.19 | -1.03 |
| Mar-08 | 5.64 | 6.32 | 4.77 | 0.17 | 5.47 | 6.15 | 4.60 |
| Apr-08 | 1.44 | 3.00 | 1.51 | 0.17 | 1.27 | 2.83 | 1.34 |
| May-08 | -7.18 | -6.25 | -8.35 | 0.17 | -7.35 | -6.42 | -8.52 |
| Jun-08 | -1.80 | -0.40 | -0.90 | 0.17 | -1.97 | -0.57 | -1.07 |
| Jul-08 | 1.37 | 0.45 | 1.55 | 0.15 | 1.22 | 0.30 | 1.40 |
| Aug-08 | -7.50 | -11.63 | -9.42 | 0.12 | -7.62 | -11.75 | -9.54 |
| Sep-08 | -18.16 | -15.45 | -16.52 | 0.15 | -18.31 | -15.60 | -16.67 |
| Oct-08 | -7.16 | -7.93 | -6.96 | 0.08 | -7.24 | -8.01 | -7.04 |
| Nov-08 | 2.70 | 0.57 | 0.99 | 0.02 | 2.68 | 0.55 | 0.97 |
| Dec-08 | -10.76 | -4.49 | -8.22 | 0.09 | -10.85 | -4.58 | -8.31 |
Excess returns have been shown in the spread sheet.
(b)
To calculate:
In this part of the problem we have to calculate standard deviation of each fund.
Explanation of Solution
Standard deviation on excel can be calculated by using formula as = stdev
Then we have to choose the data accordingly to calculate standard deviation.
|
|
Total monthly returns |
|
|
|
Excess Returns |
|
|
|
Month |
Vanguard |
Value Fund |
S&P |
T-bills |
Vanguard |
Value Fund |
S&P |
| Jan-04 | 1.52 | -0.07 | 1.35 | 0.07 | 1.45 | -0.14 | 1.28 |
| Feb-04 | -0.53 | -0.99 | -1.32 | 0.06 | -0.59 | -1.05 | -1.38 |
| Mar-04 | -2.69 | -2.46 | -1.89 | 0.09 | -2.78 | -2.55 | -1.98 |
| Apr-04 | 0.22 | 2.52 | 1.70 | 0.08 | 0.14 | 2.44 | 1.62 |
| May-04 | 2.53 | 1.39 | 1.85 | 0.06 | 2.47 | 1.33 | 1.79 |
| Jun-04 | -1.93 | -7.46 | -3.22 | 0.08 | -2.01 | -7.54 | -3.30 |
| Jul-04 | 0.99 | -0.78 | 0.25 | 0.1 | 0.89 | -0.88 | 0.15 |
| Aug-04 | 1.52 | 2.49 | 1.00 | 0.11 | 1.41 | 2.38 | 0.89 |
| Sep-04 | 0.21 | 1.46 | 1.29 | 0.11 | 0.10 | 1.35 | 1.18 |
| Oct-04 | 5.22 | 4.66 | 4.46 | 0.11 | 5.11 | 4.55 | 4.35 |
| Nov-04 | 3.24 | 3.60 | 3.01 | 0.15 | 3.09 | 3.45 | 2.86 |
| Dec-04 | -2.36 | -3.48 | -2.24 | 0.16 | -2.52 | -3.64 | -2.40 |
| Jan-05 | 3.62 | 0.79 | 2.09 | 0.16 | 3.46 | 0.63 | 1.93 |
| Feb-05 | -2.33 | -2.86 | -1.83 | 0.16 | -2.49 | -3.02 | -1.99 |
| Mar-05 | -2.68 | -2.41 | -1.87 | 0.21 | -2.89 | -2.62 | -2.08 |
| Apr-05 | 4.08 | 7.13 | 3.22 | 0.21 | 3.87 | 6.92 | 3.01 |
| May-05 | 2.25 | 0.51 | 0.15 | 0.24 | 2.01 | 0.27 | -0.09 |
| Jun-05 | 3.55 | 5.28 | 3.82 | 0.23 | 3.32 | 5.05 | 3.59 |
| Jul-05 | -1.85 | -0.85 | -0.93 | 0.24 | -2.09 | -1.09 | -1.17 |
| Aug-05 | 0.38 | 1.34 | 0.80 | 0.3 | 0.08 | 1.04 | 0.50 |
| Sep-05 | -1.88 | 0.30 | -2.36 | 0.29 | -2.17 | 0.01 | -2.65 |
| Oct-05 | 2.87 | 5.04 | 4.39 | 0.27 | 2.60 | 4.77 | 4.12 |
| Nov-05 | 0.93 | 0.46 | -0.19 | 0.31 | 0.62 | 0.15 | -0.50 |
| Dec-05 | 3.41 | 3.30 | 2.41 | 0.32 | 3.09 | 2.98 | 2.09 |
| Jan-06 | 0.00 | -1.82 | 0.57 | 0.35 | -0.35 | -2.17 | 0.22 |
| Feb-06 | 0.71 | 0.34 | 1.65 | 0.34 | 0.37 | 0.00 | 1.31 |
| Mar-06 | 0.53 | -0.45 | 1.26 | 0.37 | 0.16 | -0.82 | 0.89 |
| Apr-06 | -3.00 | -5.84 | -3.01 | 0.36 | -3.36 | -6.20 | -3.37 |
| May-06 | -0.27 | -1.55 | 0.26 | 0.43 | -0.70 | -1.98 | -0.17 |
| Jun-06 | 1.09 | -2.36 | 0.45 | 0.4 | 0.69 | -2.76 | 0.05 |
| Jul-06 | 2.70 | 3.60 | 2.18 | 0.4 | 2.30 | 3.20 | 1.78 |
| Aug-06 | 2.63 | 2.87 | 2.70 | 0.42 | 2.21 | 2.45 | 2.28 |
| Sep-06 | 2.56 | 1.92 | 3.16 | 0.41 | 2.15 | 1.51 | 2.75 |
| Oct-06 | 0.75 | 1.94 | 1.99 | 0.41 | 0.34 | 1.53 | 1.58 |
| Nov-06 | 2.32 | 0.22 | 0.77 | 0.42 | 1.90 | -0.20 | 0.35 |
| Dec-06 | 1.86 | 2.18 | 1.51 | 0.4 | 1.46 | 1.78 | 1.11 |
| Jan-07 | -2.30 | -1.69 | -1.96 | 0.44 | -2.74 | -2.13 | -2.40 |
| Feb-07 | 0.81 | 0.89 | 1.16 | 0.38 | 0.43 | 0.51 | 0.78 |
| Mar-07 | 3.87 | 2.92 | 4.42 | 0.43 | 3.44 | 2.49 | 3.99 |
| Apr-07 | 3.65 | 3.37 | 3.39 | 0.44 | 3.21 | 2.93 | 2.95 |
| May-07 | -2.02 | -1.14 | -1.46 | 0.41 | -2.43 | -1.55 | -1.87 |
| Jun-07 | -4.74 | -0.79 | -3.13 | 0.4 | -5.14 | -1.19 | -3.53 |
| Jul-07 | 1.12 | 1.11 | 1.28 | 0.4 | 0.72 | 0.71 | 0.88 |
| Aug-07 | 2.54 | 4.91 | 3.88 | 0.42 | 2.12 | 4.49 | 3.46 |
| Sep-07 | 0.39 | 2.19 | 1.35 | 0.32 | 0.07 | 1.87 | 1.03 |
| Oct-07 | -5.86 | -3.90 | -3.87 | 0.32 | -6.18 | -4.22 | -4.19 |
| Nov-07 | 0.25 | 0.00 | -1.13 | 0.34 | -0.09 | -0.34 | -1.47 |
| Dec-07 | -5.39 | -10.34 | -6.04 | 0.27 | -5.66 | -10.61 | -6.31 |
| Jan-08 | -2.67 | -2.38 | -2.58 | 0.21 | -2.88 | -2.59 | -2.79 |
| Feb-08 | -0.89 | -0.06 | -0.90 | 0.13 | -1.02 | -0.19 | -1.03 |
| Mar-08 | 5.64 | 6.32 | 4.77 | 0.17 | 5.47 | 6.15 | 4.60 |
| Apr-08 | 1.44 | 3.00 | 1.51 | 0.17 | 1.27 | 2.83 | 1.34 |
| May-08 | -7.18 | -6.25 | -8.35 | 0.17 | -7.35 | -6.42 | -8.52 |
| Jun-08 | -1.80 | -0.40 | -0.90 | 0.17 | -1.97 | -0.57 | -1.07 |
| Jul-08 | 1.37 | 0.45 | 1.55 | 0.15 | 1.22 | 0.30 | 1.40 |
| Aug-08 | -7.50 | -11.63 | -9.42 | 0.12 | -7.62 | -11.75 | -9.54 |
| Sep-08 | -18.16 | -15.45 | -16.52 | 0.15 | -18.31 | -15.60 | -16.67 |
| Oct-08 | -7.16 | -7.93 | -6.96 | 0.08 | -7.24 | -8.01 | -7.04 |
| Nov-08 | 2.70 | 0.57 | 0.99 | 0.02 | 2.68 | 0.55 | 0.97 |
| Dec-08 | -10.76 | -4.49 | -8.22 | 0.09 | -10.85 | -4.58 | -8.31 |
|
Average | -0.59 | -0.60 | -0.55 | ||||
|
Standard Deviation | 4.05 | 4.21 | 3.81 |
Standard deviation for the two funds is 4.05 and 4.21.
(d)
To Calculate:
In this question we have to calculate Sharpe, Jensen and Treynor ratio for each fund.
Explanation of Solution
All these ratios are calculated as:
Sharpe ratio=
Excess Return / standard devation
Treynor=Excess return / Beta
Jensen=αP = E(rP) − {rf + βP [E(rM) − rf]}
|
|
Total monthly returns |
|
|
|
Excess Returns |
|
|
|
Month |
Vanguard |
Value Fund |
S&P |
T-bills |
Vanguard |
Value Fund |
S&P |
| Jan-04 | 1.52 | -0.07 | 1.35 | 0.07 | 1.45 | -0.14 | 1.28 |
| Feb-04 | -0.53 | -0.99 | -1.32 | 0.06 | -0.59 | -1.05 | -1.38 |
| Mar-04 | -2.69 | -2.46 | -1.89 | 0.09 | -2.78 | -2.55 | -1.98 |
| Apr-04 | 0.22 | 2.52 | 1.70 | 0.08 | 0.14 | 2.44 | 1.62 |
| May-04 | 2.53 | 1.39 | 1.85 | 0.06 | 2.47 | 1.33 | 1.79 |
| Jun-04 | -1.93 | -7.46 | -3.22 | 0.08 | -2.01 | -7.54 | -3.30 |
| Jul-04 | 0.99 | -0.78 | 0.25 | 0.1 | 0.89 | -0.88 | 0.15 |
| Aug-04 | 1.52 | 2.49 | 1.00 | 0.11 | 1.41 | 2.38 | 0.89 |
| Sep-04 | 0.21 | 1.46 | 1.29 | 0.11 | 0.10 | 1.35 | 1.18 |
| Oct-04 | 5.22 | 4.66 | 4.46 | 0.11 | 5.11 | 4.55 | 4.35 |
| Nov-04 | 3.24 | 3.60 | 3.01 | 0.15 | 3.09 | 3.45 | 2.86 |
| Dec-04 | -2.36 | -3.48 | -2.24 | 0.16 | -2.52 | -3.64 | -2.40 |
| Jan-05 | 3.62 | 0.79 | 2.09 | 0.16 | 3.46 | 0.63 | 1.93 |
| Feb-05 | -2.33 | -2.86 | -1.83 | 0.16 | -2.49 | -3.02 | -1.99 |
| Mar-05 | -2.68 | -2.41 | -1.87 | 0.21 | -2.89 | -2.62 | -2.08 |
| Apr-05 | 4.08 | 7.13 | 3.22 | 0.21 | 3.87 | 6.92 | 3.01 |
| May-05 | 2.25 | 0.51 | 0.15 | 0.24 | 2.01 | 0.27 | -0.09 |
| Jun-05 | 3.55 | 5.28 | 3.82 | 0.23 | 3.32 | 5.05 | 3.59 |
| Jul-05 | -1.85 | -0.85 | -0.93 | 0.24 | -2.09 | -1.09 | -1.17 |
| Aug-05 | 0.38 | 1.34 | 0.80 | 0.3 | 0.08 | 1.04 | 0.50 |
| Sep-05 | -1.88 | 0.30 | -2.36 | 0.29 | -2.17 | 0.01 | -2.65 |
| Oct-05 | 2.87 | 5.04 | 4.39 | 0.27 | 2.60 | 4.77 | 4.12 |
| Nov-05 | 0.93 | 0.46 | -0.19 | 0.31 | 0.62 | 0.15 | -0.50 |
| Dec-05 | 3.41 | 3.30 | 2.41 | 0.32 | 3.09 | 2.98 | 2.09 |
| Jan-06 | 0.00 | -1.82 | 0.57 | 0.35 | -0.35 | -2.17 | 0.22 |
| Feb-06 | 0.71 | 0.34 | 1.65 | 0.34 | 0.37 | 0.00 | 1.31 |
| Mar-06 | 0.53 | -0.45 | 1.26 | 0.37 | 0.16 | -0.82 | 0.89 |
| Apr-06 | -3.00 | -5.84 | -3.01 | 0.36 | -3.36 | -6.20 | -3.37 |
| May-06 | -0.27 | -1.55 | 0.26 | 0.43 | -0.70 | -1.98 | -0.17 |
| Jun-06 | 1.09 | -2.36 | 0.45 | 0.4 | 0.69 | -2.76 | 0.05 |
| Jul-06 | 2.70 | 3.60 | 2.18 | 0.4 | 2.30 | 3.20 | 1.78 |
| Aug-06 | 2.63 | 2.87 | 2.70 | 0.42 | 2.21 | 2.45 | 2.28 |
| Sep-06 | 2.56 | 1.92 | 3.16 | 0.41 | 2.15 | 1.51 | 2.75 |
| Oct-06 | 0.75 | 1.94 | 1.99 | 0.41 | 0.34 | 1.53 | 1.58 |
| Nov-06 | 2.32 | 0.22 | 0.77 | 0.42 | 1.90 | -0.20 | 0.35 |
| Dec-06 | 1.86 | 2.18 | 1.51 | 0.4 | 1.46 | 1.78 | 1.11 |
| Jan-07 | -2.30 | -1.69 | -1.96 | 0.44 | -2.74 | -2.13 | -2.40 |
| Feb-07 | 0.81 | 0.89 | 1.16 | 0.38 | 0.43 | 0.51 | 0.78 |
| Mar-07 | 3.87 | 2.92 | 4.42 | 0.43 | 3.44 | 2.49 | 3.99 |
| Apr-07 | 3.65 | 3.37 | 3.39 | 0.44 | 3.21 | 2.93 | 2.95 |
| May-07 | -2.02 | -1.14 | -1.46 | 0.41 | -2.43 | -1.55 | -1.87 |
| Jun-07 | -4.74 | -0.79 | -3.13 | 0.4 | -5.14 | -1.19 | -3.53 |
| Jul-07 | 1.12 | 1.11 | 1.28 | 0.4 | 0.72 | 0.71 | 0.88 |
| Aug-07 | 2.54 | 4.91 | 3.88 | 0.42 | 2.12 | 4.49 | 3.46 |
| Sep-07 | 0.39 | 2.19 | 1.35 | 0.32 | 0.07 | 1.87 | 1.03 |
| Oct-07 | -5.86 | -3.90 | -3.87 | 0.32 | -6.18 | -4.22 | -4.19 |
| Nov-07 | 0.25 | 0.00 | -1.13 | 0.34 | -0.09 | -0.34 | -1.47 |
| Dec-07 | -5.39 | -10.34 | -6.04 | 0.27 | -5.66 | -10.61 | -6.31 |
| Jan-08 | -2.67 | -2.38 | -2.58 | 0.21 | -2.88 | -2.59 | -2.79 |
| Feb-08 | -0.89 | -0.06 | -0.90 | 0.13 | -1.02 | -0.19 | -1.03 |
| Mar-08 | 5.64 | 6.32 | 4.77 | 0.17 | 5.47 | 6.15 | 4.60 |
| Apr-08 | 1.44 | 3.00 | 1.51 | 0.17 | 1.27 | 2.83 | 1.34 |
| May-08 | -7.18 | -6.25 | -8.35 | 0.17 | -7.35 | -6.42 | -8.52 |
| Jun-08 | -1.80 | -0.40 | -0.90 | 0.17 | -1.97 | -0.57 | -1.07 |
| Jul-08 | 1.37 | 0.45 | 1.55 | 0.15 | 1.22 | 0.30 | 1.40 |
| Aug-08 | -7.50 | -11.63 | -9.42 | 0.12 | -7.62 | -11.75 | -9.54 |
| Sep-08 | -18.16 | -15.45 | -16.52 | 0.15 | -18.31 | -15.60 | -16.67 |
| Oct-08 | -7.16 | -7.93 | -6.96 | 0.08 | -7.24 | -8.01 | -7.04 |
| Nov-08 | 2.70 | 0.57 | 0.99 | 0.02 | 2.68 | 0.55 | 0.97 |
| Dec-08 | -10.76 | -4.49 | -8.22 | 0.09 | -10.85 | -4.58 | -8.31 |
|
Average | -0.59 | -0.60 | -0.55 | ||||
|
Sharpe ratio | -0.15 | -0.14 | -0.14 | ||||
|
Alpha | -0.03 | -0.04 | 0.00 | ||||
|
Treynor | -0.57 | -0.58 | -0.55 |
| Alpha | -0.03 | -0.04 | 0.00 |
| Treynor | -0.57 | -0.58 | -0.55 |
Want to see more full solutions like this?
Chapter 18 Solutions
ESSENTIALS OF INVESTMENTS SELECT CHAPT
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