Final presentation
The dataset “mfunds” contains the time series of returns for 9 different funds and the risk-free rate (column tbill).
Consider the usual assumptions we saw in class for returns (normal distribution and i.i.d. sample) and estimate the parameters of the normal distributions. In addition check if the i.i.d assumption is reasonable in the data.
Imagine now you can invest in the 9 assets and the risk-free asset. Compare the assets in terms of risk and return, and try to find the following:
• at least one portfolio with variance lower than the variance of any fund, both with and without investing in the risk-free asset (diversification effect).
• at least one portfolio with expeted return higher than the expeted return of any fund, both with and without investing in the risk-free asset (leveraging).
• at least one portfolio with sharpe ratio higher than the sharpe ratio of any fund, both with and without investing in the risk-free asset.
Amongst the portfolios you defined, which one pays the most per unit of risk?
NB: each portfolio doesn’t have to contain all the funds.
NB: for simplicity, instead of the column tbill, consider a constant risk-free rate equal to the mean of the colum tbill.
NB: if you want, you can consider only 3 risky assets instead of all the 9 available assets.
Optional. Which is in general the portfolio that pays the most per unit of risk? Can you find this portfolio using the given dataset?