Question
In: Finance
On Monday January 17, 2017 an investor wanted to invest $1,000,000 in two stocks Verizon (VZ)...
On Monday January 17, 2017 an investor wanted to invest $1,000,000 in two stocks Verizon (VZ) and ATT (T). Using historical adjusted weekly closes from January 2, 2016 to January 15, 2017.
a) FInd the proportions of the portfolio with minmal risk
b) As of June 23, 2017, find the market value of this portfolio and deduce the rate of return of this investment.
Solutions
Expert Solution
Answer ) The concept of portfolio :
Expected return = W1 * return 1 + W2* return 2
p2
= W12*
12 + W22*
22 + 2 *W1 W2 *
1*
2 r12
DATA as per instruction
| Date | VZ | Return(VZ) | T | Return(T) | |||
| 1/1/2016 | 40.33802 | 29.55258 | Average Return(VZ) | 0.4030% | |||
| 1/8/2016 | 40.47338 | 0.3355% | 30.67496 | 3.7979% | Average Return(T) | 0.5091% | |
| 1/15/2016 | 41.37539 | 2.2287% | 30.8896 | 0.6997% | |||
| 1/22/2016 | 44.20771 | 6.8454% | 31.77497 | 2.8662% | Standard deviation (VZ) | 0.022549 | |
| 1/29/2016 | 45.48858 | 2.8974% | 32.66928 | 2.8145% | Standard deviation (T) | 0.021593 | |
| 2/5/2016 | 44.55048 | -2.0623% | 32.3831 | -0.8760% | |||
| 2/12/2016 | 45.9486 | 3.1383% | 33.08067 | 2.1541% | Correlation | 0.769933 | |
| 2/19/2016 | 46.10195 | 0.3337% | 33.4205 | 1.0273% | |||
| 2/26/2016 | 46.80551 | 1.5261% | 33.97498 | 1.6591% | |||
| 3/4/2016 | 47.19338 | 0.8287% | 34.26116 | 0.8423% | |||
| 3/11/2016 | 48.37502 | 2.5038% | 34.98555 | 2.1143% | |||
| 3/18/2016 | 48.31188 | -0.1305% | 34.77092 | -0.6135% | |||
| 3/25/2016 | 48.78093 | 0.9709% | 35.03027 | 0.7459% | |||
| 4/1/2016 | 46.90473 | -3.8462% | 34.51157 | -1.4807% | |||
| 4/8/2016 | 46.81646 | -0.1882% | 34.78559 | 0.7940% | |||
| 4/15/2016 | 45.60413 | -2.5895% | 34.27856 | -1.4576% | |||
| 4/22/2016 | 46.50655 | 1.9788% | 34.98478 | 2.0602% | |||
| 4/29/2016 | 46.34247 | -0.3528% | 35.07532 | 0.2588% | |||
| 5/6/2016 | 46.91674 | 1.2392% | 35.80869 | 2.0909% | |||
| 5/13/2016 | 45.23951 | -3.5749% | 34.8037 | -2.8066% | |||
| 5/20/2016 | 45.72263 | 1.0679% | 35.16586 | 1.0406% | |||
| 5/27/2016 | 46.27866 | 1.2161% | 35.16586 | 0.0000% | |||
| 6/3/2016 | 47.35428 | 2.3242% | 36.29761 | 3.2183% | |||
| 6/10/2016 | 48.7307 | 2.9066% | 36.65978 | 0.9978% | |||
| 6/17/2016 | 49.83365 | 2.2634% | 37.91828 | 3.4329% | |||
| 6/24/2016 | 50.90014 | 2.1401% | 39.12247 | 3.1757% | |||
| 7/1/2016 | 50.48084 | -0.8238% | 38.29855 | -2.1060% | |||
| 7/8/2016 | 51.41402 | 1.8486% | 39.15767 | 2.2432% | |||
| 7/15/2016 | 50.98127 | -0.8417% | 38.92879 | -0.5845% | |||
| 7/22/2016 | 50.51169 | -0.9211% | 38.98372 | 0.1411% | |||
| 7/29/2016 | 49.65541 | -1.6952% | 39.44149 | 1.1743% | |||
| 8/5/2016 | 49.59095 | -0.1298% | 39.7253 | 0.7196% | |||
| 8/12/2016 | 48.67942 | -1.8381% | 37.90338 | -4.5863% | |||
| 8/19/2016 | 48.56894 | -0.2270% | 37.60125 | -0.7971% | |||
| 8/26/2016 | 48.39399 | -0.3602% | 37.50054 | -0.2679% | |||
| 9/2/2016 | 49.35156 | 1.9787% | 37.71112 | 0.5615% | |||
| 9/9/2016 | 47.85996 | -3.0224% | 37.03362 | -1.7965% | |||
| 9/16/2016 | 48.20063 | 0.7118% | 37.63787 | 1.6316% | |||
| 9/23/2016 | 47.98887 | -0.4393% | 37.28997 | -0.9243% | |||
| 9/30/2016 | 46.27629 | -3.5687% | 35.80679 | -3.9774% | |||
| 10/7/2016 | 46.83153 | 1.1998% | 36.48373 | 1.8905% | |||
| 10/14/2016 | 45.76061 | -2.2868% | 35.81653 | -1.8288% | |||
| 10/21/2016 | 45.20188 | -1.2210% | 33.84267 | -5.5110% | |||
| 10/28/2016 | 43.64672 | -3.4405% | 33.94461 | 0.3012% | |||
| 11/4/2016 | 43.4791 | -0.3840% | 33.889 | -0.1638% | |||
| 11/11/2016 | 44.55001 | 2.4631% | 34.66742 | 2.2970% | |||
| 11/18/2016 | 46.77565 | 4.9958% | 35.89065 | 3.5285% | |||
| 11/25/2016 | 46.44041 | -0.7167% | 36.02966 | 0.3873% | |||
| 12/2/2016 | 47.61376 | 2.5266% | 37.44749 | 3.9352% | |||
| 12/9/2016 | 48.247 | 1.3299% | 38.45758 | 2.6974% | |||
| 12/16/2016 | 49.96046 | 3.5514% | 39.58814 | 2.9398% | |||
| 12/23/2016 | 50.04427 | 0.1678% | 39.53254 | -0.1405% | |||
| 12/30/2016 | 50.88237 | 1.6747% | 39.52328 | -0.0234% | |||
| 1/6/2017 | 49.05717 | -3.5871% | 38.0035 | -3.8453% | |||
| 1/13/2017 | 49.45884 | 0.8188% | 38.39832 | 1.0389% |
With the concept of above metioned portfolio concept , the minimumvariance portfolio will formed as
| Portfolio combination | |||
| Case | Portion in VZ | Portion in T | Standard Deviation |
| 1 | 0.1 | 0.9 | 0.0176 |
| 2 | 0.2 | 0.8 | 0.0140 |
| 3 | 0.3 | 0.7 | 0.0108 |
| 4 | 0.4 | 0.6 | 0.0080 |
| 5 | 0.5 | 0.5 | 0.0057 |
| 6 | 0.6 | 0.4 | 0.0038 |
| 7 | 0.7 | 0.3 | 0.0023 |
| 8 | 0.8 | 0.2 | 0.0013 |
| 9 | 0.9 | 0.1 | 0.0007 |
| 10 | 1 | 0 | 0.0005 |
Clearly indicate that case 10 , maximum portion of investment in VZ will lead to minimum risk .
So, all investment is done on 17 jan 2017 in VZ shares at price of $ 49.46 /shares
No of shares = $1,000,000 / $ 49.46 = 20218.35 = 20218 shares
Answer b) As on 23 june 2017 , price of VZ share =$43.26
Value of portfolio = 20218 * $ 43.26 =$ 874630.68
Return = $ 874630.68 - $1,000,000 = -$125369
Return % = -12.54 %
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