Question

Please use the following data to answer the questions. The ticker symbols are for Tesla Inc (TSLA), Barrick Gold Corporation (GOLD) and Apple Inc (AAPL). The prices shown are the closing stock prices for the date shown. Your first task is to compute the monthly holding period returns for each stock for each month, using the Holding Period Return formula, which is HPR = (P₁ - P₀)/P₀, where P₁ is the end of period price and P₀ is the start of period price. Be very careful to not mix up your dates. After you have computed the HPRs, then answer the following ten questions.

Date	TSLA	TSLA	GOLD	GOLD	AAPL	AAPL
2019-07-01	$ 241.61		$    16.26		$213.04
2019-08-01	$ 225.61		$    19.38		$208.74
2019-09-01	$ 240.87		$    17.33		$223.97
2019-10-01	$ 314.92		$    17.36		$248.76
2019-11-01	$ 329.94		$    16.80		$267.25
2019-12-01	$ 418.33		$    18.59		$293.65
2020-01-01	$ 650.57		$    18.52		$309.51
2020-02-01	$ 667.99		$    19.04		$273.36
2020-03-01	$ 524.00		$    18.32		$254.29
2020-04-01	$ 781.88		$    25.72		$293.8
2020-05-01	$ 835.00		$    24.00		$317.94
2020-06-01	$ 985.98		$    25.73		$364.84

What is the sample standard deviation of the portfolio comprised of 40% TSLA, 30% GOLD and 30% AAPL? Use the Variance/Covariance Matrix to assist in this calculation.

Multiple Choice

• 13.4%

• 12.9%

• 11.6%

• 15.1%

What is the geometric mean of the monthly stock returns for TSLA?

Multiple Choice

• A)16.6% B) 16.7% C) 13.6% D) 14.8%

What is the standard deviation of the sample of monthly stock returns for TSLA?

Multiple Choice

• A) 21.9% B) 23.2% C) 35.2% D) 47.1%

Assume you had invested $10,000 in TSLA July 1, 2019, the first date of the sample. What would your investment be worth on the last date of the period?

Multiple Choice

• A) $40,659 B) $45,639 C) $62,967 D) $34,645

What is the correlation of the stock returns between TSLA and GOLD?

Multiple Choice

• 0.70

• 0.50

• 0.60

• 0.40

Now assume that your portfolio is invested 40% in TSLA, 30% in GOLD and 30% in AAPL. What return would you expect for this portfolio, using the formula for portfolio return.

Multiple Choice

• 8.5%

• 10.7%

• 9.4%

• 4.4%

Answer 1

1]

variance for a three-asset portfolio σ_p² = w₁²σ₁² + w₂²σ₂² + w₃²σ₃²+ 2w₁w₂Cov_1,2 + 2w₂w₃Cov_2,3 + 2w₁w₃Cov_1,3

where σ_p² = variance of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

w₃ = weight of Asset 3

σ₁² = variance of Asset 1

σ₂² = variance of Asset 2

σ₂² = variance of Asset 2

Cov_1,2 = covariance of returns between Asset 1 and Asset 2

Cov_2,3 = covariance of returns between Asset 2 and Asset 3

Cov_1,3 = covariance of returns between Asset 1 and Asset 3

Variance and covariance are calculated using VAR.S and COVARIANCE.S functions in Excel

Standard deviation = $\sqrt{}$ variance

Standard deviation = 13.4%

2]

geometric mean is calculated by adding 1 to each month's HPR, calculating the geometric mean of that series by using GEOMEAN function in Excel, and finally subtracting 1 from the GEOMEAN calculated above.

geometric mean is 13.6%

3]

Standard deviation is calculated using STDEV.S function in Excel

Standard deviation is 23.2%

4]

value of investment on last date = amount invested * (share price on last date / share price on first date)

value of investment on last date = $10,000 * ($ 985.98 / $ 241.61)

value of investment on last date = $40,809

5]

correlation is calculated using CORRfunction in Excel

correlation is 0.40

6]

Expected return of 3-asset portfolio R_p = w₁R₁ + w₂R₂ + w₃R₃

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2

w₃ = weight of Asset 3

R₃ = expected return of Asset 3

Expected return of each asset is the arithmetic average.

Expected return = (40% * 15.74%) + (30% * 5.07%) + (30% * 5.36%)

Expected return = 9.4%

А B с Date TSLA TSLA - HPR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 7/1/2019 $241.61 8/1/2019 $225.61 9/1/2019 $240.87 10/1/2019 $314.92 11/1/2019 $329.94 12/1/2019 $418.33 1/1/2020 $650.57 2/1/2020 $667.99 3/1/2020 $524.00 4/1/2020 $781.88 5/1/2020 $835.00 6/1/2020 $985.98 Average Geom. Mean Std.Dev. -6.62% 6.76% 30.74% 4.77% 26.79% 55.52% 2.68% -21.56% 49.21% 6.79% 18.08% 15.74% 13.6% 23.2% D E F H TSLA - (1 GOLD - AAPL - GOLD AAPL + HPR) HPR HPR $16.26 $213.04 0.9338 $19.38 19.19% $208.74 -2.02% 1.0676 $17.33 -10.58% $223.97 7.30% 1.3074 $17.36 0.17% $248.76 11.07% 1.0477 $16.80 3.23% $267.25 7.43% 1.2679 $18.59 10.65% $293.65 9.88% 1.5552 $18.52 -0.38% $309.51 5.40% 1.0268 $19.04 2.81% $273.36-11.68% 0.7844 $18.32 -3.78% $254.29 -6.98% 1.4921 $25.72 40.39% $293.80 15.54% 1.0679 $24.00 -6.69% $317.94 8.22% 1.1808 $25.73 7.21% $364.84 14.75% 5.07% 5.36% AAPL 0.012818517 0.003391285 18 Covariance TSLA GOLD 19 TSLA 0.013396108 20 GOLD 21 AAPL 22 23 TSLA GOLD 24 Variance 0.053979014 0.020718261 25 Weight 0.40 0.30 26 0.008636642 0.001864644 27 0.003215066 0.000610431 28 Std.Dev. 13.4% AAPL 0.00757957 0.30 0.000682161 0.003076444 29 30 Correlation 0.40

A B с D E F G H Date TSLA TSLA - HPR TSLA - (1 + HPR) GOLD GOLD - HPR AAPL JAAPL - HPR 1 2 43647 343678 4 43709 5 43739 6 43770 7 43800 8 43831 9 43862 10 43891 11 43922 12 43952 13 43983 14 241.61 225.61 240.87 314.92 329.94 418.33 650.57 667.99 524 781.88 835 985.98 Average Geom. Mean Std.Dev. =(B3-B2)/B2 =(B4-B3/B3 =(B5-B4)/B4 =(B6-B5)/B5 =(B7-B6)/B6 =(B8-B7)/B7 =(B9-B8)/B8 =(B10-B9y/B9 =(B11-B10)/B10 =(B12-B11)/B11 =(B13-B12)/B12 =AVERAGE(C3:C13) =GEOMEAN(D3:D13)-1 =STDEV.S(C3:C13) =1+C3 = 1+C4 =1+C5 =1+C6 =1+C7 = 1+C8 =1+C9 =1+C10 =1+C11 =1+C12 =1+C13 16.26 19.38 17.33 17.36 16.8 18.59 18.52 19.04 18.32 25.72 24 25.73 213.04 =(E3-E2)/E2 208.74)=(G3-G2/G2 =(E4-E3)/E3 223.97 )=(G4-G3/G3 =(E5-E4/E4 248.76 =(G5-G4)/G4 =(E6-E5)/E5 267.25 =(G6-G5)/G5 =(E7-E6/E6 293.65 =( G7-G6)/G6 =(E8-E7)/E7 309.51 =(G8-G7)/G7 =(E9-E8)/E8 273.36 =(G9-G8)/G8 =(E10-E9)/E9 254.29 =(G10-G9/G9 =(E11-E10)/E10 293.8 =(G11-G10)/G10 =(E12-E11)/E11 317.94 =(G12-G11)/G11 =(E13-E12)/E12 364.84 =(G13-G12)/G12 =AVERAGE(F3:F13) =AVERAGE(H3:H13) 15 16 AAPL =COVARIANCE.S(C3:C13,H3:H13) =COVARIANCE.S(F3:F13,H3:H13) 18 Covariance TSLA GOLD 19 TSLA =COVARIANCE.S(C3:C13,F3:F13) 20 GOLD 21 AAPL 22 23 TSLA GOLD 24 Variance =VAR.S(C3:C13) =VAR.S(F3:F13) 25 Weight 0.4 0.3 26 =(B25^2) *B24 =(C25^2) *C24 27 =2*B25*C25*C19 =2*C25*E25*E20 28 Std.Dev. =SQRT(SUM(B26:E27)) 29 30 Correlation =CORREL(C3:C13,F3:F13) AAPL =VAR.S(H3:H13) 0.3 =(E25^2) *E24 =2*B25*E25*E19