Picking up where we left off in yesterday's FFRHX CVaR Portfolio Optimization Part I, we will now optimize the Leveraged Loan Mutual Fund FFRHX, using Conditional Value at Risk (CVaR) Optimization.
FFRHX is a leveraged loan Mutual Fund with relatively low risk, the fund managers have chosen this path by holding almost 15% of their assets in cash. The fund has average expenses for its category with a ratio of 0.71 percent; however it does have a redemption fee of 1.00% if you redeem within 60 days, and a minimum investment of $2,500.00. The minimum balance is $2,000.00, but you are unlikely to hit that amount as volatility is low.
The ETF’s chosen for this optimization were from the Leveraged Loan family, or the high yield debt family, both asset classes that are held predominantly in the Mutual Fund. They listed below with their symbol, name and expense ratio.
· ($BKLN): Senior Loan Portfolio, .66%
· (EMHY) : Emerging Markets High Yield Bond Fund, .65%
· ($HYS): 0-5 Year High Yield Corporate Bond Index Fund, .55%
· (QLTC) : B-Ca Rated Corporate Bond Fund, .30%
· ($HYG): iShares iBoxx $ High Yield Corporate Bond ETF, .50%
· ($PHB): Fundamental High Yield Corporate Bond Portfolio, .50%
· ($BSJD): Bulletshares 2013 High Yield Corporate Bond ETF, .42%
· ($BSJE): Bulletshares 2014 High Yield Corporate Bond ETF, .42%
· ($BSJF): Bulletshares 2015 High Yield Corporate Bond ETF, .42%
· ($BSJG): Bulletshares 2016 High Yield Corporate Bond ETF, .42%
· ($BSJH): Bulletshares 2017 High Yield Corporate Bond ETF, .42%
· ($BSJI): Bulletshares 2018 High Yield Corporate Bond ETF, .42%
· ($ANGL): Market Vectors Fallen Angel ETF, .40%
· (GHYG) : Global High Yield Corporate Bond Fund, .65%
· ($HYEM): Market Vectors Emerging Markets High Yield Bond ETF, .40%
· ($HYXU): Global ex USD High Yield Corporate Bond Fund, .40%
· ($IHY): Market Vectors International High Yield Bond ETF, .40%
· ($JNK): SPDR Barclays Capital High Yield Bond ETF, .40%
· ($SJNK): SPDR Barclays Capital Short Term High Yield Bond ETF, .40%
· (QLTB) : Baa-Ba Rated Corporate Bond Fund, .30%
The optimization for this is achieved slightly differently than the traditional Mean-Variance method. Since CVaR is slightly more sensitive than standard deviation, we have optimized over monthly returns as opposed to annual returns. This does mean that for more advanced investors, with larger sums of money at stake, portfolio adjustments are occasionally necessary. As a result I will adjust this portfolio monthly, and we will keep track of the performance and risk in relation to the Mutual Fund. Below is the efficient frontier for the FFRHX optimization:
This efficient frontier is similar to the Mean Variance frontier, with the only difference being the x axis. If you recall, the blue line is like a wall for the possible portfolios. Using optimization technique, we have established that no portfolio without leverage can achieve a better trade off of risk versus return. The return is obviously the same, but the proxy for risk in this case is CVaR as opposed to the standard deviation of the portfolio.
We have two portfolios listed on the efficient frontier, in traditional format for these articles they are a low risk portfolio and a lower risk portfolio. They are listed below.
.8% Monthly Return .14% Monthly Return
($HYS), 26% (QLTC) , 26%
($BSJD), 5% ($HYXU), .74%
($HYXU), 21%
($SJNK), 48%
The weighted expense ratios for the .8% portfolio and .14% portfolios were .44% and .374% respectively. When compared to the .71% expense ratio for the Mutual Fund, you are cutting costs by a significant amount. In addition, the Mutual Fund only returns .35% monthly, so you are beating it in returns in both instances. While the CVaR of the Mutual Fund is a little lower at .006, CVaR is not quite as easy to interpret as standard deviation. Both are extremely low numbers, and considering the almost complete lack of movement from FFRHX, the ETF Portfolio becomes a much better choice.
