Tag Archives: investing

A New Sector ETF Defends Against Rising Rates On The Cheap

10-year Treasury yields have begun pricing in that view by soaring nearly 8.5 percent over the past month. With rising rates right around the corner (maybe), investors might want to have a look at a new financial services ETF, XLFS. Another way of looking at XLFS is that the new ETF is XLF without real estate stocks, an important feature. By Todd Shriber, ETF Professor As investors have come to grips with the fact that it is highly likely that the Federal Reserve will finally raise interest rates next month, 10-year Treasury yields have begun pricing in that view by soaring nearly 8.5 percent over the past month. Although financial services stocks, on a historical basis, have questionable reactions to increases in borrowing costs, conventional wisdom holds that the sector is positively correlated to higher interest rates. The corresponding exchange traded funds are reflecting that thesis as the Financial Select Sector SPDR ETF (NYSEARCA: XLF ), the largest financial services ETF, is higher by 2.1 percent over the past month. With rising rates right around the corner (maybe), investors might want to have a look at a new financial services ETF, the Financial Services Select Sector SPDR ETF (NYSEARCA: XLFS ) . The Financial Services Select Sector SPDR, which debuted last month, was brought to market ahead of real estate becoming the 11th Global Industry Classification Standard (GICS) sector. That change is scheduled to occur after markets close on August 31, 2016. In November 2014, S&P Dow Jones Indices and MSCI, two of the largest providers of indices for use with ETFs, announced real estate – previously included as part of the financial services group – would become its own sector . Another way of looking at XLFS is that the new ETF is XLF without real estate stocks, an important feature when considering real estate equities are vulnerable to rising interest rates and currently richly valued relative to the broader market. According to AltaVista Research data, the Real Estate Select Sector SPDR ETF (NYSEARCA: XLRE ) , which debuted with XLFS, has an estimated 2015 price-to-earnings ratio of 36.4 compared to 17.8 for the S&P 500. Underscoring how much of a difference real estate exposure makes in terms of valuation, the P/Es for XLFS and XLF are 12.9 and 14.4, respectively. Remember, XLFS does not hold real estate stocks, but XLF does. “Financial Services firms have made steady improvements in profitability (margins and ROE) since the Financial Crisis, and with lower leverage hopefully they will be more stable as well. Given the robust, double-digit long-term EPS growth projections and reasonable valuation multiples, the sector looks attractive at these levels,” said AltaVista. The research firm rates XLFS neutral. Warren Buffett’s Berkshire Hathaway Inc. (NYSE: BRK.B ) and Wells Fargo & Co. (NYSE: WFC ) combine for over 20 percent of XLFS’s weight. Other top 10 holdings include Bank of America Corp. (NYSE: BAC ) and Citigroup Inc. (NYSE: C ). Disclaimer: Neither Benzinga nor its staff recommend that you buy, sell, or hold any security. We do not offer investment advice, personalized or otherwise. Benzinga recommends that you conduct your own due diligence and consult a certified financial professional for personalized advice about your financial situation.

Portfolio Rebalancing: 2 Approaches And A Practical Example

Summary A well-constructed, diversified portfolio typically starts with a well designed asset allocation plan. Similar to a garden or landscape, however, entropy can leave your portfolio looking like it had no plan, with potentially frightening implications for your risk level. I will create and track a hypothetical portfolio, expose the risks of leaving it in an untended state, and walk through two variants of rebalancing over a five-year term. I will offer practical suggestions that you may be able to apply to your own portfolio. Finally, I will offer a few thoughts on cost and tax considerations, as well as links to suggested further reading. I think most investors would agree that having a sound asset allocation plan is a large factor in success, particularly when taking a long-term view and working towards a goal that will ultimately have a real and measurable impact on the quality of one’s life. For example, when I built The ETF Monkey Vanguard Core Portfolio , I diversified into three very different asset classes: 1) Domestic Stocks, 2) Bonds, and 3) Foreign Stocks. When doing so, I did not just randomly select some allocation percentage pulled out of thin air. Instead, I used Vanguard’s Target Retirement 2035 Fund (MUTF: VTTHX ) to select a suitable asset allocation for a 45-year-old, with approximately 20 working years until retirement. Portfolio Drift and the Need to Rebalance However, much like the landscape around your home, your asset allocation needs regular maintenance. When you landscaped your home (or started a garden, as the case may be), you likely worked with design and installation professionals to pick exactly the right plants for each location depending on your climate zone, the correct sun/shade mix and similar factors. No doubt, it all looked absolutely spectacular upon completion. However, left untended, your landscape or garden will not look nearly as good even weeks later, not to mention a year or more. In fact, it might ultimately look so bad that it would be hard for an impartial observer to discern that there had ever been a design or plan. People with a scientific mind call this entropy, one definition of which is “a gradual decline into disorder.” Your asset allocation, left untended, is also subject to entropy. Another way to phrase this is “portfolio drift.” Fundamentally, this is not a bad thing. Likely, you purposely designed your portfolio such that it was diversified, which typically means it contains asset classes with low correlation ; where one may outperform at the same time another underperforms. Over time, however, this behavior can result in your asset classes drifting far from their initial weighting. In turn, this has the potential to raise the risk level of your portfolio far beyond what you ever intended. Let’s take a look in the rear view mirror, so to speak, at a hypothetical portfolio constructed on October 31, 2010. In this portfolio, our investor selected the following investments: A 35% weighting in the S&P 500 index, intended to form a solid foundation of large-cap domestic stocks. An “adventurous” weighting of 10% in the NASDAQ index, in an attempt to spice up the overall return of the portfolio. A 20% weighting in the FTSE 100 index, to gain some exposure to foreign equities. A 35% weighting in a total market bond offering. Note: For our purposes, please don’t get hung up on whether these were four great choices, the proposed weightings or anything else like that. I simply used these because they serve well to make the main point of this article. I am also ignoring the effects of any dividends received and the resulting cash balance. In the picture below, have a look at how those asset classes performed over the five years ending October 31, 2015: ^SPX data by YCharts From one perspective, this is all wonderful. Certainly, we are happy to have the 76.38% return generated from the S&P 500 index, and we are positively ecstatic over the 102.2% return from the NASDAQ index. The next picture shows the actual results of this hypothetical portfolio, assuming an initial investment of $100,000. (click to enlarge) The good news is that our $100,000 has grown to $138,859. In large part, this is a result of the amazing performance of U.S. stocks over the past five years. Now for the bad news. Take a look at the “Current Weight” column. You will note that I feature two numbers in bold red. The weighting of the S&P 500 index now stands at 44.46%, almost 10% above our well-designed plan! Let’s go a step further. The S&P and NASDAQ indexes, combined, now comprise $81,953, or 59.02% of our portfolio, almost 15% above our intended weight of 45%. Conversely, the other two asset groups, foreign equities and bonds, are now horribly under-represented. Foreign equities are underweight about 4% and bonds by more than 10%! As featured, this is a double-edged sword. We are happy for the returns we received. At the same time, were there to be a sharp downturn in the U.S. market, we might be shocked the next time we opened our statement. Also, were the FTSE index to move up nicely in a positive direction, our underweight allocation would cause us to miss out on the full intended benefit. Before we move on, ponder this thought as it relates to why our hypothetical portfolio looks the way it does. The asset classes that offer the greatest returns tend to have the greatest volatility . You may notice that, with a 45.6% variance, in percentage terms the NASDAQ index has strayed the farthest from its original weighting. In other words, the asset classes that give you the best chance for outsized returns also offer the greatest potential for leaving your portfolio in a far riskier place than you ever intended. Sadly, while the example in this article is hypothetical, the problem is real. For example, with respect to 401(k) plans, according to this 2014 article : A recent TIAA CREF survey found that 25% of workers have never made changes to how their money is invested and an additional 28% have not made changes . . . in more than one year. The answer, of course, is to periodically rebalance the portfolio. This simply means that funds are taken from the asset classes that have outperformed and moved to those that have underperformed, such that each asset class is restored to its original weighting. Let us next look at two ways to do so. Time-Based Rebalancing: A Simple Example The simplest form of rebalancing is time-based , or period-based , rebalancing. In this version, the investor selects a specified interval of time at which to rebalance the portfolio. This is a common option offered in 401(k) plans. The investor may choose to do so in an automated fashion; perhaps once per quarter, six months, or year. What, though, are the effects of rebalancing on a portfolio? In the picture below, I will show the results of performing a simple annual rebalancing transaction on our hypothetical portfolio. Following the picture, I will share several observations with you. (click to enlarge) To begin with, for the benefit of readers who may wish to verify the accuracy of my work, allow me to first explain my methodology. I used the same YCharts tool used to generate the “5-Year” view of the portfolio displayed as the first picture in the article. However, I changed the periods to one year at a time, starting with the period 10/31/2010 – 10/31/2011, and continuing in the same fashion until I got to 10/31/2014 – 10/31/2015. Each row of green boxes represents one year, from left to right. The value displayed in the Annual Return Column represents the return for each asset class for the given period. I then show the Current Balance based on those returns, and the Current Weight of each asset class before rebalancing. In the rightmost box, I show the amount of the rebalancing transaction, and the New Balance after all asset classes are restored to their original weighting. Finally, I reference the New Balance as the Initial Investment for the next year and repeat the process. Now, some observations on the performance of the portfolio. First, please note that this rebalancing strategy is “brainless” in the sense that no active thought or research goes into its implementation. A date is simply set on the calendar, and the portfolio is rebalanced. Next, if you are like most investors, you likely noted that you have $4,013 less ($138,859 vs. $134,846) in the rebalanced version than in the untended version. This leads to a “theoretical vs. real-world” issue with rebalancing, as follows: Theory: A diversified portfolio contains asset classes whose returns should offset each other over time. Therefore, if you rebalance from the best-performing groups into those that underperform, not only should your portfolio contain lower volatility but you may even improve your returns. Practice: Not that simple. In the case of our portfolio, U.S. stocks (S&P & NASDAQ) significantly outperformed both of the other asset classes (FTSE and Bonds) over an extended period of time. Therefore, our consistent annual rebalancing exercise moved assets into classes that continued to underperform. However, it is good to remember exactly what I featured, namely that our hypothetical example was performed over a time period where U.S. stocks soundly outperformed virtually any other asset class. In some ways, this was a “worst case” scenario for disciplined rebalancing. At the same time, we are in a far better position should U.S. stocks be subjected to a severe, and possibly extended, stretch of underperformance. Recall that in our untended portfolio, fully 59.02% of our assets were in U.S. stocks. In our rebalanced portfolio, we are only at 46.44%, not far from our target allocation of 45%. Threshold-Based Rebalancing: A Simple Example A more “active” variant of rebalancing is threshold-based rebalancing. In this variant, we actively monitor the portfolio and rebalance at any time an asset class deviates from its target weighting by some set percentage. I wish to make clear at the outset that this is not blatant market timing. In other words, it is not going all-or-nothing into one asset class or another on a “bet” that we will achieve higher returns. Instead, we are simply “buying low and selling high” according to how the markets, and our chosen asset classes, behave. Let’s see how this variant works out using a simple example of threshold-based rebalancing of the same portfolio. In this example, everything is the same as in our time-based example except that I only rebalanced once, at the end of Year 3. (click to enlarge) I purposely kept this example very simple in the hopes of making it very easy to follow and understand. You will notice that I used the same five annual periods as in the first example. Therefore, the periods and returns are exactly the same. The only thing I did differently was apply a hypothetical deviation threshold of 5%. In other words, I would “let my winners ride” until an asset class deviated by at least 5% from my target allocation. If you look at Year 1, this did not happen. So, I just let the portfolio carry on without rebalancing. The end of Year 2 rolled around and, still, no asset class had deviated by 5%. Even my overall weighting in domestic stocks (S&P 500 and NASDAQ) had not deviated by 5%. Once again, I stood pat. In Year 3, however, spectacular returns in the S&P asset class drove it to a 41.28% weighting, a deviation of 6.28% from my target allocation. So, I rebalanced everything. In Years 4 and 5, once again we did not experience a 5% deviation based on the portfolio as rebalanced at the end of Year 3. So, I stood pat on both occasions. As you can see, this slightly more active involvement resulted in, arguably, the best of both worlds. My portfolio balance is $136,305, some $1,459 above the time-based variant and $2,554 below my rather “fortunate” untended portfolio. At the same time, no asset class is horribly over or underweighted. I might note that, at a weighting of 50.82% for the S&P 500 and NASDAQ combined, my overall U.S. stock weighting has a deviation of more than 5% from my target allocation, so I certainly might consider rebalancing once again at this time. Again, though, the choice is mine. Threshold-Based Rebalancing: Fine-Tuning the Concept In the simple example above, while I employed threshold-based rebalancing, I only examined the portfolio once a year, on October 31. Clearly, that doesn’t take full advantage of the technique, as the market does not somehow magically select October 31 as the best day of the year to rebalance. With that in mind, take one more look at the picture below. It’s the same 5-Year YCharts graph I developed to start the article. However, I captured a screen shot of that image and then added some arrows. (click to enlarge) The arrows above the line (pointing downwards) feature specific points along the way at which we may have been interested in selling certain overvalued asset classes. In contrast, the arrows below the line (pointing upwards) feature specific points at which we may have been interesting in buying into undervalued asset classes. Since, however, most of us don’t have crystal balls with which to predict the future, how do we know when such opportunities manifest themselves? To answer this question, allow me to share a high-level glimpse into my own portfolio. As can be seen, at the present time I break my portfolio into, and track, seven separate asset classes. In total, my portfolio contains 20 components (16 ETFs and 4 individual stocks). The pictured summary comes from an Excel spreadsheet I have built for myself. The spreadsheet originates from a download of my portfolio (in .CSV file format for you techies) from the Fidelity website. I then use Excel’s tools to sort and subtotal the data by symbol. I “tag” each symbol with the correct asset class. Finally, what you see here simply summarizes it all. The purpose of this entire exercise is to develop the two rightmost columns in the summary above. These reveal the extent of deviation of each asset class from its target. Let me explain those two columns explicitly. The Difference column reveals the actual difference in the weighting percentage. So, in the case of Utilities, 5.22% exceeds the 5.00% target by .22%. The %Diff column represents the percentage of variance . So, 5.22% is 104.30% of 5.00%. The last column is the one I focus on. My personal approach is that when the percentage of variance of any asset class varies by 5% from its target weight , it goes on my radar as a possible candidate for rebalancing. This helps put the greatly differing weightings of my asset classes into big-picture perspective. In other words, at 40% of my total, my Domestic Stocks allocation has to deviate by 2% to have a 5% deviation in percentage terms. At only 5% of my total, my Utilities allocation only has to vary by .25% to hit the same relative threshold of deviation. (NOTE: Again, for you Excel techies, you can use Conditional Formatting on cells like this to, for example, turn the cell yellow if the value exceeds 105% and red if it exceeds 110%. This is no biggie, it just gives you a visual cue when targets are hit.) In summary, I view this as what I call “Active management of a passive portfolio.” Other Considerations When Rebalancing The last thought I wish to leave you with is a reminder that various costs are involved in rebalancing, and you need to factor these in when making your ultimate decisions. For this discussion, I will feature just two: 1) Trading costs and 2) Tax consequences. Trading Costs – In many cases, you may invoke some level of trading commissions to execute your rebalancing transaction(s). So, let’s go back to my Utilities groups. At only 5% of my portfolio, I shared previously that the weighting only has to deviate by .25% to achieve a 5% deviation in percentage of variance. At the same time, this may not be a large amount in dollar terms. Therefore, I may have to exercise some judgment in deciding whether the cost of rebalancing the asset class is justified. In my case, as a Fidelity Brokerage client, I get around a lot of this by using commission-free ETFs for the major asset classes. As an example, I use the iShares Core S&P Total U.S. Stock Market ETF (NYSEARCA: ITOT ) and the iShares Core MCSI Total International Stock ETF (NYSEARCA: IXUS ) as commission-free tools to rebalance my weighting in Domestic Stocks and Foreign Stocks. Tax consequences – To the extent that your investments are in taxable accounts, you must also be aware of the tax consequences of rebalancing. In the case of our hypothetical portfolio, clearly we had gains, perhaps even substantial gains, in our S&P 500 and NASDAQ positions. To the extent that these are long-term in nature, one can benefit from the lower long-term tax rates. Whatever the case, however, this must factor into your ultimate decision. Summary and Conclusion I hope that you have found this article helpful, from both a theoretical and practical perspective. I have discussed the reasons to rebalance an investment portfolio, shared two variants of rebalancing a hypothetical portfolio to hopefully expose some pros and cons, offered some practical suggestions on how to track and evaluate your own portfolio, and closed with a couple of cautions with respect to the various costs of rebalancing. Happy investing! Further Reading U.S. Securities and Exchange Commission – Beginners’ Guide to Asset Allocation, Diversification, and Rebalancing Smith Barney Consulting Group – The Art of Rebalancing The Vanguard Group – Best Practices For Portfolio Rebalancing

Towards A Zero-Beta Stocks And Bonds Portfolio

Summary A low-risk investor may want to completely remove systematic risk associated with stock market trends (i.e. achieve portfolio beta of 0). You can do this by pairing an S&P 500 mutual fund or ETF with any negative-beta bond fund. The necessary allocation to the S&P 500 fund is given by c = beta / (beta – 1), where beta is the bond fund’s beta. The beta of a bond fund changes over time. One approach is to use a trailing 50-day moving average to estimate your bond fund’s current beta. Backtested performance of a zero-beta SPY/TLT strategy suggest very good raw and risk-adjusted returns since mid-2002 (CAGR 7.2%, MDD 21.4%, Sharpe ratio 0.049). Alpha and Beta of a Two-Fund Portfolio Alpha and beta are the intercept and slope, respectively, when you regress a fund or portfolio’s daily gains vs. daily gains for a standard index. In this article, I use the SPDR S&P 500 Trust ETF ( SPY) as the standard index. For a portfolio with some allocation to two different funds, the portfolio alpha is simply the weighted average of the two funds’ alphas, and the portfolio beta is the weighted average of the two funds’ betas. For example, suppose you pair SPY, which has alpha of 0 and beta of 1 by definition, with a bond fund that has alpha of 0.002% and beta of -0.1. If you allocated 25% to SPY and 75% to the bond fund, your portfolio alpha would be 0.25 (0%) + 0.75 (0.002%) = 0.0015%, and your portfolio beta would be 0.25 (1) + 0.75 (-0.1) = 0.175. One can show that when pairing SPY with a bond fund with some particular beta, the necessary SPY allocation for portfolio beta of 0 is given by c = beta / (beta – 1). Why Target Zero Beta? It may sound strange, but a portfolio with net beta of 0 on average moves 0% for every 1% change in the S&P 500. In other words, it has no dependence on market movement. Generally when investors add exposure to bonds they retain some positive net beta, but much smaller than 1. By reducing beta, they shield themselves from major portfolio losses in the event that the stock market takes a big dip, while also sacrificing raw returns if the stock market performs well and gains, say, 8% a year. With beta of 0, you theoretically completely shield your portfolio from any market movement. Does that mean 0% portfolio gain every day? Thankfully, no. A zero-beta portfolio comprised of a stocks fund and a bond fund has positive alpha due to the bond allocation, which gives the portfolio growth potential. SPY and TLT Consider a two-fund stocks and bonds portfolio comprised of SPY and the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ). If you pool together all daily gains going back to TLT’s inception in July 2002, TLT has alpha of 0.043% and beta of -0.297. That means that various allocations to SPY and TLT can achieve portfolio alphas between 0% and 0.043%, and portfolio betas between -0.297 and 1. The figure below illustrates this. (click to enlarge) We see that 22.9% SPY/77.1% TLT achieves a portfolio beta of 0, with a nice portfolio alpha of 0.033%. Note that 22.9% agrees with our formula for SPY allocation to achieve zero beta: c = beta / (beta – 1) = -0.297 / (-0.297 – 1) = 0.229. In terms of Sharpe ratio, we’re doing pretty well at 22.9% SPY, although Sharpe ratio is maximized at 40.7%. But our goal here is zero beta, so we stick with 22.9% SPY. Note that alpha decreases uniformly with increasing beta in this scenario, since increasing beta requires decreasing the TLT allocation and capturing a lower percentage of its alpha. Historical Performance of 22.9% SPY/77.1% TLT Performance of the zero-beta SPY/TLT portfolio (with free daily rebalancing) since inception is shown below. (click to enlarge) The zero-beta portfolio ended above TLT and slightly below SPY, but had much better risk-adjusted performance, as you can see below. Table 1. Performance metrics from July 30, 2002, to Nov. 3, 2015. Fund CAGR (%) Max Drawdown (%) Sharpe ratio SPY 8.6% 55.2% 0.033 TLT 7.2% 26.6% 0.036 22.9% SPY/77.1% TLT 8.3% 19.3% 0.055 Issues With 22.9% SPY/77.1% TLT Portfolio Two issues with the zero-beta SPY/TLT portfolio come to mind: Actual beta changes over time, because TLT’s beta changes. There is no way we could have predicted that the SPY allocation to achieve average beta of 0 from 2002-2015 was 22.9%. Issue (1) means our zero-beta portfolio’s beta is not always 0. For example, here is how the TLT’s beta, and the 22.9% SPY/77.1% TLT portfolio’s beta, vary over the backtested period, using a 50-day moving average. (click to enlarge) We see that TLT’s beta varies quite a bit (-1.05 to 0.45). The 22.9% SPY/77.1% TLT portfolio’s beta range is smaller (-0.58 to 0.58), but still too great for a supposed zero-beta portfolio. A First Crack at a Truly Zero Beta SPY/TLT Portfolio A natural solution to both issues (1) and (2) is to monitor TLT’s beta over time, and update the asset allocation accordingly. For a first attempt I’ll arbitrarily choose a 50-day trailing moving average. Every day, I’ll calculate TLT’s beta according to the previous 50 daily gains, and re-allocate if the current portfolio beta based on the SPY and TLT balance and TLT’s current beta is outside of (-0.15, 0.15). But what happens when TLT’s beta turns positive? In that case there is no way to achieve zero beta with SPY and TLT. Three options come to mind: Hold cash until TLT’s beta turns negative again. Allocate 100% to TLT, since that is the closest to zero beta we can achieve with SPY/TLT and we utilize all of TLT’s alpha. Swap SPY for an inverse S&P 500 ETF (e.g. SH) to achieve zero beta. I think this is an important topic for future work. The third seems most defensible, but for simplicity I’ll use (2) here. TLT’s beta was only positive about 16% of the time, so it may not make a huge difference. The next figure shows portfolio beta for the adaptive zero-beta SPY/TLT strategy based on 50-day trailing moving averages. (click to enlarge) Much better. The 22.9% SPY/77.1% TLT portfolio and the adaptive zero-beta SPY/TLT portfolio had actual betas outside of (-0.1, 0.1) 63.3% and 43.1% of the time, respectively; outside of (-0.2, 0.2) 38.2% and 18.2% of the time; and outside of (-0.3, 0.3) 19.0% and 6.9% of the time. However, the adaptive strategy did require a whopping 1,264 trades, or an average of about 97 trades per year. I didn’t incorporate trading costs into this backtest, but they would be substantial unless your portfolio balance was very high. In terms of the usual performance metrics, the adaptive strategy had CAGR of 7.2%, MDD of 21.4%, and Sharpe ratio of 0.049. Note that if you only rebalance when portfolio beta goes outside of (-0.3, 0.3) rather than (-0.15, 0.15), you “only” need 618 trades (48 per year), but your portfolio beta deviates more from 0. That portfolio had a backtested CAGR of 8.6%, MDD of 26.6%, and Sharpe ratio of 0.052. Implementation Details Implementing this strategy takes a little work. Every day, you would have to download SPY and TLT’s closing prices for the past 50 days, calculate daily gains, and estimate TLT’s beta. You would then have to calculate your portfolio’s effective beta, and adjust your allocations if necessary. It isn’t actually too hard to do this. You can estimate TLT’s trailing 50-day beta in a few lines of R code using my “stocks” package. First install the package (you only have to do this once): > install.packages(“stocks”) Then load it and call the beta.trailing50 function: > library(“stocks”) > beta.trailing50(“TLT”) Then you’d have to log into your investments account, get your current SPY and TLT allocation, and calculate your effective beta (SPY allocation * 1 + TLT allocation * current beta). If effective beta is out of range, calculate the target SPY allocation (c = beta / (beta – 1)) and rebalance accordingly. It’s not ideal, but it really only takes a few minutes. My sense is that you could monitor TLT’s beta and your portfolio’s beta a little less stringently (e.g. once a month rather than every day) and still do all right. I plan to test this in future work. Conclusions I really like the idea of having a portfolio with considerable growth potential but no systematic dependence on stock market trends. TLT is a good candidate to pair with SPY for this purpose, because it is has positive alpha and negative beta. TLT’s average beta since inception is -0.297, which means you need to allocate 22.9% to SPY and 77.1% to TLT to achieve zero beta. Such a portfolio had excellent performance since 2002, but wasn’t entirely satisfactory because the actual beta often deviated far from 0, and you couldn’t have known to allocate 22.9% to SPY during that 13-year period to achieve average zero beta. While it may not be the optimal solution, I found that you could keep the portfolio beta much closer to 0 by monitoring TLT’s beta using a trailing 50-day moving average. Future work will focus on comparing the three approaches mentioned for when TLT’s beta turns positive, and on adjustments to keep the portfolio beta as close to zero as possible without suffering excessive trading costs.