Correlation.. covariance.. I am so lost This monday I'll take my exam in Investment analyses. My teacher usually gives a matrix with covariances and beta's, which makes it easy to find Expected return/ Variance. He just posted some exam prep questions. I've been failing to solve some of them. Any chance somebody could try to safe the day?
Given:
The annual expected excess return on the market
portfolio equals 5.50% with a volatility of 13% and the risk free rate is 2% annually. 
Risky asset A Risky asset B Market Portfolio
Cov Asset A and B is 0.0116 
Cov Asset A and market is 0.0154
Cov Asset B and market is 0.0115
Correlation between asset A and the market portfolio is 0.95 and the
correlation between asset B and the market portfolio is 0.63. 
-> Capm holds 
-> Equal weighted portfolio (50% A 50% B)
Calculate Expected return and volitility.
I'm not expecting anybody to solve the questions for me. I'm just very confused how to determine Variance with the given information. Anybody got any tips how to solve this?  
 A: Given your (poorly written) question, I can try and gauge what you've asked.
Given the CAPM holds, we know:
$$\begin{align}
E[R_{i}]&=R_{f}+\beta_{i}(E[R_{M}]-R_{f})
\end{align}$$
where $E[R_{i}]$ is the expected return on asset $i$, $R_{f}$ is the risk-free rate of interest, $E[R_{M}]$ is the expected return on the market and $\beta_{i}$ is the sensitivity of the excess returns of the asset to excess returns of the market.
Using very basic portfolio theory, a portfolio comprised of weights, $w_{i}$, of Asset A and Asset B has return:
$$\begin{align}
R_{p}&=w_{A}R_{A}+w_{B}R_{B}
\end{align}$$
Taking the expectation gives:
$$\begin{align}
E[R_{p}]&=w_{A}E[R_{A}]+w_{B}E[R_{B}]
\end{align}$$
The variance of the portfolio is given by:
$$\begin{align}
\text{Var}(R_{p})&=\text{Var}(w_{A}R_{A}+w_{B}R_{B})\\
&=w_{A}^{2}\text{Var}(R_{A})+w_{B}^{2}\text{Var}(R_{B})+2w_{A}w_{B}\text{Cov}(R_{A},R_{B})
\end{align}$$
Keep in mind the relationship between $\beta_{i}$, $\text{Cov}(R_{i})$ and $\text{Var}(R_{M})$:
$$\begin{align}
\beta_{i}&=\frac{\text{Cov}(R_{i},R_{M})}{\text{Var}(R_{M})}\\
\end{align}$$
And that generally:
$$\begin{align}
\rho_{R_{i},R_{j}}&=\frac{\text{Cov}(R_{i},R_{j})}{\sqrt{\text{Var}(R_{i})\text{Var}(R_{j})}}\\
\end{align}$$
where $\rho_{R_{i},R_{j}}$ is the correlation coefficient between $R_{i}$ and $R_{j}$.
