1- Interpret the results of Variance- covariance matrix and the correlation matr

Question

1- Interpret the results of Variance- covariance matrix and the correlation matrix? why do these results tell you?

2- Interpret the standard deviation of portfolio returns and bitcoin returns? why do these results tell you?

04. the variance-covariance matrix and correlation matrix are sp500. Returns emmrkt.returns metals.returns btcxts.returns sp500.Returns 5.935872e-05 1.932038e-05 -6.314173e-06 2.895578e-07 emmrkt.returns 1.932038e-05 6.632641e-05 -2.100514e-06 6.784204e-06 metals.returns 6. 314173e-06 2.100514e-06 6.736465e-05 7.780220e-06 btcxts.returns 2.895578e-07 6.784204e-06 7.780220e-06 1.678462e-03 sp500.Returns emmrkt.returns metals.returns btcxts.returns sp500.Returns 1.00000000-0.17571552 0.04074418 -0.01919035 emmrkt.returns 0.17571552 1.00000000 0.01382630 0.03261315 metals.returns 0.04074418 0.01382630 1.00000000 0.02708290 btcxts.returns 0.01919035 0.03261315 0.02708290 1.00000000 5b. the standard deviation of portfolio returns and bitcoin returns [1] 0.01073718 Standard deviation of portfolio returns [1] 0.03821432 Standard deviation of bitcoin

Explanation / Answer

Part 1) The variance-covariance matrix and correlation matrix tell us TWO main things:-

1. Variances: The diagonal elements are the self-variances of each variable. "What is the deviation from mean value?"

- The Bitcoin returns vary MUCH MORE than the returns of the other indices/portfolios.

2. Co-variances: The non-diagonal elements are the co-variances of a pair of variables. "How do any pair of variables vary together?" If positive, one variable increases with increase in the other variable. If negative, the variable decreases with an increase in the other variable.

- The metal index and the emmrkt index returns have a positive co-variance with bitcoin returns

- But, the metal index and emmrkt index returns themselves have a negative co-variance with each other

- sp500 returns have negative co-variance with every other mentioned portfolio/index

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Part 2) Standard deviation of Bitcoin returns is much larger than that of portfolio returns which means that the returns vary a lot more than those of portfolio => Bitcoin is a more VOLATILE investment

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