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Portfolio Optimization With Leveraged Bond Funds

Summary Bond funds are great because they generate alpha and usually have negative correlation with stocks. Using the leveraged version of a bond fund can drastically improve portfolio optimization (i.e. produce greater expected returns for a given level of volatility). I use SPY/TLT and SPY/TMF to illustrate. SPY/TLT Portfolio Optimization Consider a two-fund portfolio optimizaton problem based on the SPDR S&P 500 ETF Trust (NYSEARCA: SPY ) and the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ). Often the goal is to maximize the ratio of expected returns to volatility (Sharpe ratio). I don’t like that approach, because when you maximize Sharpe ratio, you tend to get a portfolio with great risk-adjusted returns but relatively small raw returns. Instead, let’s say the goal is to choose an asset allocation that maximizes expected returns for some level of volatility that you can tolerate. A good way to do that is to look at a plot of mean vs. standard deviation of daily returns for various asset allocations. Here is that plot using SPY and TLT data going back to 2002. (click to enlarge) The red curve shows mean and standard deviation of daily portfolio gains for various asset allocations. The points represent 10% asset allocation increments. The top-right point is 100% SPY, 0% TLT; the next point is 90% SPY, 0% TLT; and so on until the bottom-most point on the other end of the curve, which is 0% SPY, 100% TLT. Suppose you want no more than three-fourths the volatility of SPY, or a standard deviation no greater than 0.93%. Looking at the graph, we want to be right around the third data point from the upper-right end of the curve. That data point represents 80% SPY, 20% TLT. This is the optimal allocation for an investor who wants to maximize returns at three-fourths the volatility of SPY. SPY/3x TLT Portfolio Optimization Let’s see how replacing TLT with a perfect 3x daily TLT fund (no expense ratio, no tracking error) affects the portfolio optimization problem. (click to enlarge) The red curve shows the same data as in the first figure, it just looks different because I had to zoom out to accommodate the SPY/3x TLT curve. Here I show asset allocations in 5% increments for the blue curve. The lowest point on the blue curve is 100% SPY, 0% 3x TLT; the next point is 95% SPY, 5% 3x TLT; and so on until the rightmost point, which is 0% SPY, 100% 3x TLT. Interestingly, increasing 3x TLT exposure from 0% reduces volatility and increases mean returns up until about 25% 3x TLT. Over the volatility range 0.884%-1.235%, you can do substantially better in terms of maximizing mean returns for a given level of volatility with SPY/3x TLT compared to SPY/TLT. Going back to the first example, at a volatility of 0.93%, or three-fourths the volatility of SPY, the best mean return you can achieve with SPY/TLT is 0.039%, with 80.1% SPY and 19.9% TLT. The best you can do with SPY/3x TLT is 0.059%, with 65.5% SPY and 34.5% 3x TLT. Daily returns of 0.059% and 0.039% correspond to CAGRs of 16.0% and 10.3%, respectively. For another interesting special case, suppose you can tolerate the volatility of SPY. With SPY/TLT, the optimal portfolio is 100% SPY and 0% TLT, with a mean daily return of 0.040%. With SPY/3x TLT, the optimal portfolio is 48.4% SPY and 51.6% 3x TLT, with a mean daily return of 0.069%. Also noteworthy is the fact that SPY/3x TLT portfolios are capable of achieving volatility greater than SPY, while SPY/TLT portfolios are not. This could be appealing to aggressive investors. A Real 3x Bond Fund: TMF So far, I’ve shown that a perfect 3x daily TLT fund would be extremely useful for portfolio optimization. The next question is whether such a fund exists, and how “perfect” it is in regard to expense ratio and tracking error. There are a few options, but I think the most relevant is the Direxion Daily 20+ Year Treasury Bull 3x Shares (NYSEARCA: TMF ). TMF was introduced on April 16, 2009, and has a net expense ratio of 0.95%. The next figure shows that indeed TMF effectively multiplies daily TLT gains by a factor of 3. The correlation between actual TMF gains and 3x TLT gains over TMF’s 6.5-year lifetime is 0.996. (click to enlarge) I realize that TMF does not attempt to track 3x TLT, but rather 3x the NYSE 20 Year Plus Treasury Bond Index (AXTWEN). But practically speaking TMF operates very much like a 3x TLT ETF. Let’s go ahead and re-examine the mean vs. standard deviation plot for SPY/TLT, SPY/3x TLT, and SPY/TMF over TMF’s lifetime. (click to enlarge) This is interesting, and slightly disappointing. As in the previous plot, we see that SPY/3x TLT achieves drastically better mean returns for particular levels of volatility compared to SPY/TLT. The orange curve for SPY/TMF is also higher than SPY/TLT, but not as much so as SPY/3x TLT. It seems that TMF’s reasonable expense ratio and tiny tracking error do detract somewhat from the optimization problem. But we still see that increasing exposure to TMF from 0% to about 20% reduces volatility and increases expected returns, and SPY/TMF does much better than SPY/TLT for those who can tolerate volatility between 0.722% and 1.022%. Leveraged Bond Funds Multiply Alpha and Beta As I’ve argued in other articles (e.g. SPY/TLT and SPXL/TMF Strategies Work Because of Positive Alpha, not Negative Correlation ), the reason bond funds compliment stocks so well is that they generate positive alpha. A bond fund with zero or negative alpha has no place in any portfolio; you would be better off using cash to adjust volatility and expected returns. Anyway, bond funds are special because they generate alpha. Ignoring tracking error and expense ratio, a leveraged version of a bond fund multiples both the alpha and beta of the underlying bond index. We can see this with TLT and TMF. Over TMF’s lifetime, their alphas are 0.061 and 0.173, and their betas are -0.492 and -1.493, respectively. TMF’s alpha is 2.84 times that of TLT’s, and its beta is 3.03 times that of TLT’s. 3x greater alpha does not immediately render 3x TLT the better choice for portfolio optimization. You have to look at the effect on both expected returns and volatility, which are both functions of alpha and beta. Suppose you can achieve the same portfolio volatility with c allocated to SPY and (1-c) to TLT, or with d allocated to SPY and (1-d) to 3x TLT. If you subtract the expected return of the SPY/TLT portfolio from the expected return of the SPY/3x TLT portfolio, you get: (d-c) E[X] + [3(1-d) – (1-c)] E[Y] where X represents the daily return of SPY, and Y the daily return of TLT. Whether this expression is positive or negative depends on d, c, E[X], and E[Y] (which can also be expressed as alpha + beta E[X]). For SPY and TLT, the expression is always positive, which means that SPY/3x TLT provides better expected returns than SPY/TLT for any level of volatility that both can achieve. Conclusions Leveraged bond funds appear to be extremely useful for portfolio optimization. In the case of SPY and TLT, we saw that using a 3x version of TLT, like TMF, allows us to: Improve expected returns for a particular level of volatility. Achieve the same volatility as SPY, but with drastically better expected returns. Take on extra volatility beyond SPY’s in pursuit of greater raw returns. In practice, TMF’s expense ratio and tracking error detract somewhat from the performance of an ideal SPY/3x TLT portfolio. But SPY/TMF still allows for substantial improvements over SPY/TLT in terms of maximizing returns for a given level of volatility.

A High-Yield Option For Income Investors

Investing in financial markets has become considerably more difficult since the summer. High yielding assets, as well as stocks have taken a beating. Market Vectors High-Yield Muni ETF, however, has seen a steady increase in principal, while providing an attractive dividend yield. As the Treasury yield curve has contracted, alongside falling equity markets, investors have been left with few avenues to invest. Higher yielding dividend stocks, generally yielding below 3%, have seen declines in principle due to the most recent equity market rout. Additionally, junk bonds have seen broad selling pressure as investors shunned riskier assets for fear of slowing economic activity. A lone star, however, has emerged in the form of the Market Vec tors High-Yield Municipal Index ETF (NYSEARCA: HYD ) . This asset has risen close to 4% since early July, while yielding a dividend of 4.81%. This combination of appreciation of principle, as well as stable dividend yield, could be a smart play for investors seeking income in coming months. With the Federal Reserve stuck to its zero-bound lending rate, income investors have had trouble finding sustainable income sources. The global economy continues to weaken, alongside the persistence of foreign central banks loosening monetary policy, causing the Fed to potentially have trouble hiking rates in the near future. The chart below is of the iShares 7-10 Year Treasury Bond ETF (NYSEARCA: IEF ) over the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ) . This indicator represents the Treasury yield curve. When the indicator declines, it signals a contraction of the yield curve, and thus lowered expectations of a rate hike for monetary policy. Since peaking in the summer of 2015, slowing economic growth, and global financial market volatility has spooked Fed members, forcing them to push out their projected time frame for hiking rates. Furthermore, with investors continuing to buy bonds, yields have fallen to levels providing very little income for investors. (click to enlarge) Moreover, financial market volatility has pushed both junk bonds, and broader equity markets lower. Investors feel that equity markets have topped globally, and the combination of falling currencies, and commodities signal that global growth concerns are finally resulting in increased caution. While dividend stocks may be outperforming the market on a relative basis, these companies are still losing value in 2015. As U.S. earnings season disappoints, investors are pushing all sectors lower. Additionally, weak equity market performance is weighing on junk bonds as risk sentiment diminishes. After my degradation of basically every asset class, there seems to be one lone performer that has provided true safe-haven status. High yielding municipal bonds have outperformed as investors favor the comfort of government backed securities, alongside an attractive yield. As municipalities have lowered their leverage in recent years, their perceived stability has risen. This index also does a nice job of spreading risk, allowing investors to get exposure to a basket of riskier municipal bonds, with lower overall default risk. The Market Vectors High-Yield Muni ETF has proven a strong investment amid the recent volatility in bonds, equities, and currencies. As long as the Fed prolongs raising rates, and financial markets remain volatile, this high yielding municipal ETF should provide steady gains. (click to enlarge)

TLT: Think Long Term

Many retail investors find it easier to access and buy bond funds or bond ETFs instead of going out andowning individual pieces of paper debt. It has been a dull few years for bond investors. As equity prices have risen higher since 2007 and 2008, bond performance has struggled. For the course of the long term, we remain very bullish on U.S. treasury bonds, and we recommend TLT – think long term. By Parke Shall Bonds can sometimes be tricky for the average retail investor. They are usually priced much higher than stocks, sometimes around $1000 if you want to buy individual bonds, sometimes higher. It’s for that reason that many retail investors find it easier to access and buy bond funds or bond ETFs instead of going out and owning individual pieces of paper debt. There are a growing number of bond ETFs that you can put your money into, but the most important thing to look at is always whether or not these ETFs are levered and what the fees are going to cost you. Bond instruments for the long term should not have leverage, and should simply track the yields of the type of bonds that you want to invest in, whether it is municipal bonds, corporate bonds, or our favorite; government bonds. Here is a list of some of the more popular treasury bond ETFs, from ETF Database , (click to enlarge) Our preference is the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ). It has been a dull few years for bond investors. As equity prices have risen higher since 2007 and 2008, bond performance has struggled. This does not discourage us, however, as our bond investment strategy is to buy long term treasury bonds where we think there is eventually going to be some pricing support and some safety. Our investing strategy is one that always has some exposure to the consistent coupon of bonds. We try to keep some cash, we definitely keep equities, but we always do try and have varying amounts of exposure to bonds as well. Treasury bond prices have fallen, and the latest bit of news from the world of treasury bonds was that China was curbing the amount of money that they were pouring into U.S. government debt. Zerohedge said : As BNP’s Mole Hau put it on Monday, “whereas the daily fix was previously used to fix the spot rate, the PBoC now seemingly fixes the spot rate to determine the daily fix, [thus] the role of the market in determining the exchange rate has, if anything, been reduced in the short term. ” And a reduced role for the market means a larger role for the PBoC and that, in turn, means burning through more FX reserves to steady the yuan. Translation and quantification (with the latter coming courtesy of SocGen): as part of China’s devaluation and subsequent attempts to contain said devaluation, China has sold a gargantuan $106 (or more) billion in U.S. paper just as a result of the change in the currency regime. Notably, that means China has sold as much in Treasurys in the past 2 weeks – over $100 billion – as it has sold in the entire first half of the year. Today, we got what looks like confirmation late in the session when Bloomberg, citing fixed income desks, reported “substantial selling pressure in long end Treasuries coming from Far East.” We believe this move, on China’s part, is due to China needing to access the cash that it has in order to stabilize its stock market. When we look out over a broader term, we believe that Bond prices treasury bond prices will eventually study. Another interesting fact directing the bond market is the fact that inflation is seemingly nonexistent. This makes bond investing even more attractive, we believe. Short-term yields may stay at levels that they are at now for a little while to come. When the Federal Reserve finally gets around to raising rates,Will expect find pricing to begin stick up once again. However, for the course of the long term, we remain very bullish on U.S. treasury bonds, and we recommend TLT – think long term.