Use the monthly data September 2013 November 2014 provided

Use the monthly data (September 2013 - November 2014) provided on the closing prices for Gold (GLD), NASDAQ, Oil (USO) and Facebook (FB).

1)What is the risk as measured by the standard deviation of monthly return for Facebook during the sample period?

2)What is the correlation between prices of Gold and NASDAQ during the sample period?

3)What is the approximate value of mean absolute error (MAE) of forecasting based on 3 days moving average for Facebook prices?

4)What is the approximate value of mean absolute percantage error (MAPE) of forecasting based on 3 days moving average for NASDAQ

Solution

2.the correlation between prices of Gold and NASDAQ during the sample period is measured by

r=COV(gold,nasdaq)/sqrt(Var(gold)*var(nasdaq))

we have 15 values for each

now COV(gold,nasdaq)=-735.6

var(gold)=26.267   and var(nasdaq)=70312.71

hence r=-735.6/sqrt(26.267*70312.71)=-0.541 [answer]

3. let A_t be the original values of FB prices and F_t be the forecasted values of FB for t=1,2,,.....

F_t are calculated by 3 days moving average method.

i.e, at first we calculate the average of the first 3 values ,then exclude the first one and include the 4th one and calculate the average and so on until we reach the last 3 values.

these averages are the F_t which corresponds to the mid value of the three point taken.

we have

A_t    F_t

50   *
50   49.0000
47   50.6667
55   55.0000
63   62.0000
68   63.6667
60   62.6667
60   61.0000
63   63.3333
67   67.6667
73   71.6667
75   75.6667
79   76.3333
75   76.0000
74   *

MAE is given as MAE=[|A₂-F₂|+|A₃-F₃|+....+|A₁₄-F₁₄|]/13   [since the F₁ and F₁₅ can not be determined using moving average method]

so putting the values we get MAE=[|50-49|+|47-50.667|+.....+|75-76|]/13=3.6667 [answer]

4. the 3 days moving average forecast values are obtained by the same logic as mentioned in part 3.

we have

A_t       F_t

3771   *
3920   3917.00
4060   4052.33
4177   4113.67
4104   4196.33
4308   4203.67
4199   4207.33
4115   4185.67
4243   4255.33
4408   4340.33
4370   4452.67
4580   4481.00
4493   4568.00
4631   4612.33
4713   *

the MAPE is given as 100*[|A₂-F₂|/A₂+|A₃-F₃|/A₃+.........+|A₁₄-F₁₄|/A₁₄]/13 [since the F₁ and F₁₅ can not be determined using moving average method]

putting the values we have MAPE=100*[|3920-3917|/3920+|4060-4052.33|/4060+.......+|4631-4612.33|/4631]/13=1.83 [answer]

1. the monthly returns for FB are calculated as

1st month=[(closing price of FB in oct-13)-(closing price of FB in sep-13)]/(closing price of FB in sep-13)=(50-50)/50

2nd month=[(closing price of FB in nov-13)-(closing price of FB in oct-13)]/(closing price of FB in oct-13)=(47-50)/50

and so on in this way.....

14th month=[(closing price of FB in nov-14)-(closing price of FB in oct-14)]/(closing price of FB in oct-14)=(74-75)/75

in this way 14 values of the monthly returns are obtained.

the standard deviation of these 14 values would give the measurement of risk

these 14 value are

0.000000
-0.060000
0.170213
0.145455
0.079365
-0.117647
0.000000
0.050000
0.063492
0.089552
0.027397
0.053333
-0.050633
-0.013333

hence the risk=the standard deviation=0.075876 [answer]