Question

In this assignment, we will construct the best possible portfolio for an investor using one risky asset and the riskless asset. For the purposes of this assignment, the risk free rate is 3.5%. I have provided you with historical data about the returns of the risky asset. The column yearly.return contains yearly returns for each year in our sample, formatted as decimals. This means that a 10% yearly return would appear as 0.10.

A.Using the historical data provided, estimate the mean and standard deviation of the returns of the risky asset
B.Create a function that calculates the best possible asset allocation between the risky and riskless assets
C.Using this function, find the best possible asset allocation between the risky asset from Step 1 and the riskless asset for an investor with a coefficient of risk aversion of 3.8. Include the answer to this question as a comment in your script
D.Make sure to comment your script and include the name of everyone in your group in the comments
E.Upload your script

Answer 1

We will estimate the mean and standard deviation of the returns for a risky asset to understand its expected rate of return and risk, then create a function to calculate the optimal investment mix with a riskless asset at a 3.5% rate, factoring in the investor's risk aversion.

Step-by-step explanation:

In this assignment, we will construct the best possible portfolio for an investor using one risky asset and the riskless asset. The process begins with estimating the mean and standard deviation of the returns of the risky asset using historical data. The mean represents the expected rate of return, and the standard deviation measures the investment's risk, or how much the actual returns can differ from the expected returns.

Next, we will create a function to determine the best asset allocation between the risky and riskless assets. This allocation will be based on the investor's coefficient of risk aversion, a measure of the investor's willingness to take risks. For an investor with a coefficient of risk aversion of 3.8, this function will calculate the proportion of the portfolio that should be invested in the risky asset versus the riskless asset, which in this context has a guaranteed return rate of 3.5%.

The riskless asset offers security with its guaranteed rate, while the risky asset’s potential for higher returns compensates for its higher risk. By combining both, we aim to balance the trade-off between risk and return to suit the investor's preferences and achieve the best possible portfolio outcome.