Financial risks faced by investors and financial institutions

Empirical Results – Efficient Frontier
Figure 4: Efficient Portfolio Frontier

• Efficient portfolio frontier is the plot of all the best potential portfolios returns relative to their risk. In other words, each point of the plot, pictures the higher return for a given level of risk.
• To plot the efficient frontier, we rely on the model of maximize mean-variance objective function, without specific target portfolio return, using 131 monthly returns. The maximum expected return (A) of the portfolio (0.017010) is achieved at the point of the efficient frontier. In the contrary, to find the lower point of efficient frontier we minimize the mean-variance objective function without specific target portfolio return, using 131 monthly returns. The minimum expected return (MVP) of the portfolio (0.005760) is achieved at the point of the efficient frontier.
• For plotting the intermediate part of the efficient frontier, we find the trade-off between risk and return at 8 intermediate points (every of which represents different combinations of risk and return), divided the interval of maximum expected return and minimum expected return (0.017010, 0.005760) at 8 equal length sub-intervals. Investors who demand higher yields on their investments usually select portfolios that lie around the upper part of frontier and investors who demand risk diversification and lower level of risk, select to invest in portfolios from the lower part of frontier. The following figure illustrates the efficient portfolio frontier.

Empirical Results – Back Testing

• At next step we apply a back testing process to the data for a 2-years period (January 2018 - December 2019). The examined period of back testing process consists of 24 consecutive monthly periods. We construct portfolios which asset allocation change on monthly basis by following the given optimal weights. The return of these portfolios is illustrated in the following plots and compared with the index return during the same period.
• As illustrated in these figures, the monthly returns of all portfolios indicates that the trend of returns is not completely indifferent, but most of times all portfolios have similar direction in their trends (positive or negative) but in another percentage unit.
• The defensive portfolio has a return of 0.39% on average during that period. The largest monthly increase is registered on March 2019 (6.03%), while the largest decrease on December 2018 (-7.29%). The range of returns is: 6.03% - (-7.29%) = 13.32%.
• The neutral portfolio has a return of 0.93% on average, larger than the defensive portfolio’s return. The largest monthly increase is registered on January 2019 (9.86%), while the largest decrease on December 2018 (-8.43%), the same month with the defensive portfolio. The range of returns is: 9.86% - (-8.43%) = 18.29%.
• The Index portfolio has a return of 0.11% on average, smaller than both the defensive and the neutral portfolios. The largest monthly increase is registered on April 2019 (6.86%), while the largest decrease on October 2018 (-6.75%). The range of returns is: 6.86% - (-6.75%) = 13.61%.
• By comparing the three portfolios, we conclude that the neutral portfolio registered the largest return on average, following by the defensive and the Index portfolio. The neutral portfolio is also the more volatile. Furthermore, we notice that when we compare the portfolios in pairs, the monthly returns of neutral-Index portfolios are more intensely synchronized than the monthly returns of defensive-neutral portfolios and defensive-Index portfolios. This is consistent with the results, as we calculated the covariance between the neutral and the Index portfolios which is 0.001129, larger than the covariance between the defensive and the neutral portfolios (0.0008) as well as the covariance between the defensive and the Index portfolios (0.0009).

Thanks!
Any questions ?