Reference no: EM133074774

Consider an equally weighted portfolio consists as the following stocks:

• Microsoft (MSFT)
• Intel (INTC)
• International Business Machines (IBM)
• Apple Inc. (AAPL)
• Google (Alphabet Inc.) (GOOG)

and two factors

• S&P 500 Index (^GSPC)
• NASDAQ Index (^IXIC)

Let R₁, R₂, R₃, R₄, R₅ be returns of those five stocks, respectively, F₁ and F₂ be the daily returns of S&P 500 Index and NASDAQ Index.

1. Parametric VaR  (Use 1 year daily  from Yahoo Finance from 09/15/2019 to 09/15/2020)
   1. Find mean and variance of returns of 5 stocks, respectively. 
   2. Find the covariance matrix of the 5 stock returns.
   3. Consider an equally weighted portfolio of the 5 stocks and calculate parametric 99%-VaR and CVaR of the portfolio using the Gaussian assumption.
2. Historical VaR  (Use 10 years daily data from Yahoo Finance from 09/15/2010 to 09/15/2020)
   1. Find historical  99% -VaRs for those 5 stock returns. 
   2. Consider an equally weighted portfolio of the 5 stocks and calculate Historical 99%-VaR and CVaR
3. VaR with the multi-factor model  (Use 1 year daily  from Yahoo Finance from 09/15/2019 to 09/15/2020)
   1. Estimate the intercepts and beta coefficients for each R_n using regression model
   2. Find the covariance metrics for F₁ and F₂
   3. Consider an equally-weighted portfolio with those 5 stocks and Calculate 99%-VaR and CVaR (AVaR) under the Gaussian assumption.