Question

Q6: What is the Correlation Coefficient (Say between two stock returns over time)? How do standard deviations and covariance interact in this equation (show equation)? What is the correlation between stocks/bond market returns, and inflation/inflation expectations/interest rates over time? What does a -1, 0, and +1 correlation mean? Show equation and answer all questions! Q7: Show the Portfolio Standard Deviation (equation). Say for total returns on assets in a stock portfolio. Show equation! --What would HIGH covariance between stocks in the portfolio have on the portfolio standard deviation? --What would LOW covariance between stocks in the portfolio have on the portfolio standard deviation?

Answer 1

6) Correlation co-efficient measures the degree of co-movement between 2 variables over time.

Correlation(X,Y) = Covariance (X,Y) / Standard Deviation of X *Standard deviation of Y

X,Y - 2 variables/stocks

Stocks and bond market returns are positively correlated with one another and are negatively correlated with inflation/inflation expectations/interest rates as when interest rates fall, bond prices increase and stocks also increase as a result.

Inflation, inflation expectations and interest rates are positively correlated with one another.

Correlation of -1 means perfect negative correlation which means the two assets move in exact opposite direction

Correlation of 0 means the two assets are uncorrelated.

Correlation of +1 means perfect positive correlation which means the two assets move in exact same direction

7) Portfolio Standard deviation for 3 asset portfolio =Square Root of [ w1²σ1² + w2²σ2² + w3²σ3² + 2w1w2cov12 + 2w1w3cov13 + 2w2w3cov13 ]

where, wi = weight of asset i

σi = projected standard deviation (risk) of asset i.

Covij = projected covariance of asset i and asset j.

HIGH covariance between stocks in the portfolio lead to higher portfolio standard deviation

LOW covariance between stocks in the portfolio lead to lower portfolio standard deviation