So, we can see the result, the portfolio return has the same trend with the market return,
SPY’s return is always higher than MSCI, because SPY represents the better performing
US stock market. Under this portfolio1, it beats the market for only two years.
After shortening the length of the last year's volatility to the last quarter, Portfolio 2 shows
it to be less probability to beating the market. We think that the shorter time interval can
reflect the true situation of the next year and low volatile of the data, provide more
accurate risk prediction, thus selecting a better portfolio which will lead to the lower
uncertainty. so that, it is less possible to beats the market.
For the next portfolio, we use beta instead of standard deviation to measure the risk.
Because beta only represent systematic risk, portfolio3’s return curve is more closer with
those two markets. Also, it shows little probability to beat the market.
so, we can conclude......
In order to give investors with 6 risk aversion recommendation, we calculate the utility for
our three portfolios and two markets, we can see the result from the table that while
portfolio3 has highest utility, it still lower than the spy, thus we recommend investors stay
fully invested in the SPY.