Question

In: Finance

Below you find the monthly closing prices for SP500 and Amazon for 2 years 01.01.2018                         ...

Below you find the monthly closing prices for SP500 and Amazon for 2 years

01.01.2018                          2'823.81                          1'450.89
01.02.2018                          2'713.83                          1'512.45
01.03.2018                          2'640.87                          1'447.34
01.04.2018                          2'648.05                          1'566.13
01.05.2018                          2'705.27                          1'629.62
01.06.2018                          2'718.37                          1'699.80
01.07.2018                          2'816.29                          1'777.44
01.08.2018                          2'901.52                          2'012.71
01.09.2018                          2'913.98                          2'003.00
01.10.2018                          2'711.74                          1'598.01
01.11.2018                          2'760.17                          1'690.17
01.12.2018                          2'506.85                          1'501.97
01.01.2019                          2'704.10                          1'718.73
01.02.2019                          2'784.49                          1'639.83
01.03.2019                          2'834.40                          1'780.75
01.04.2019                          2'945.83                          1'926.52
01.05.2019                          2'752.06                          1'775.07
01.06.2019                          2'941.76                          1'893.63
01.07.2019                          2'980.38                          1'866.78
01.08.2019                          2'926.46                          1'776.29
01.09.2019                          2'976.74                          1'735.91
01.10.2019                          3'037.56                          1'776.66
01.11.2019                          3'140.98                          1'800.80
01.12.2019                          3'230.78                          1'847.84
  • Convert the monthly closing prices to returns
  • estimate beta with using a market risk premium 5.4%.
  • Use a current Risk-free rate from the market for your calculations and specify which instrument (type and maturity) you use.

Solutions

Expert Solution

The return table looks like this

Month S&P 500 S&P Monthly Returns Amazon Amazon Monthly Returns
01.01.2018 2,823.81 1,450.89
01.02.2018 2,713.83 -3.89% 1,512.45 4.24%
01.03.2018 2,640.87 -2.69% 1,447.34 -4.30%
01.04.2018 2,648.05 0.27% 1,566.13 8.21%
01.05.2018 2,705.27 2.16% 1,629.62 4.05%
01.06.2018 2,718.37 0.48% 1,699.80 4.31%
01.07.2018 2,816.29 3.60% 1,777.44 4.57%
01.08.2018 2,901.52 3.03% 2,012.71 13.24%
01.09.2018 2,913.98 0.43% 2,003.00 -0.48%
01.10.2018 2,711.74 -6.94% 1,598.01 -20.22%
01.11.2018 2,760.17 1.79% 1,690.17 5.77%
01.12.2018 2,506.85 -9.18% 1,501.97 -11.13%
01.01.2019 2,704.10 7.87% 1,718.73 14.43%
01.02.2019 2,784.49 2.97% 1,639.83 -4.59%
01.03.2019 2,834.40 1.79% 1,780.75 8.59%
01.04.2019 2,945.83 3.93% 1,926.52 8.19%
01.05.2019 2,752.06 -6.58% 1,775.07 -7.86%
01.06.2019 2,941.76 6.89% 1,893.63 6.68%
01.07.2019 2,980.38 1.31% 1,866.78 -1.42%
01.08.2019 2,926.46 -1.81% 1,776.29 -4.85%
01.09.2019 2,976.74 1.72% 1,735.91 -2.27%
01.10.2019 3,037.56 2.04% 1,776.66 2.35%
01.11.2019 3,140.98 3.40% 1,800.80 1.36%
01.12.2019 3,230.78 2.86% 1,847.84 2.61%
Avg Monthly Return 0.67% 1.37%
Annual Return (Monthly Return x12) 8.07% 16.41%

Cost of Equity Re = Rf + Beta x Market risk premium

Where:

Re = Cost of Equity

Rf = Risk free rate

Risk premium = (Market Return - Risk Free rate)

Prevailing 10 year treasury rate in US = 0.70% (Risk Free Rate)

Market Return = 8.07% (Annual return of S&P 500)

Return on Amazon = 16.41%

Cost of Equity Re = Rf + Beta x Market risk premium**  

Using the above values

16.41% = 0.70% + Beta x (8.07% - 0.70%)

Beta of Amazon

= (16.41% - 0.70%) / 7.37%

= 15.71% / 7.37%

= 2.13

** Since we have already calculated the market return (S&P 500 return = 8.07%), we should not use the 5.40% market risk premium. We can derive market risk premium = 8.07% - 0.70% = 7.37%


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