Tag Archives: upro

The Real Cost Of Hedging With Leveraged ETFs

Summary Scaled hedging has some advantages over usual market-timing. Leveraged ETFs are convenient hedging tools, but they suffer from a decay. This article calculates the additional cost of hedging a stock portfolio with leveraged ETFs. A timed, scalable hedging tactic has at least 3 advantages over usual market-timing consisting in going out of the market: adaptability to the risk level, lower transaction costs, and cashing all dividends. This previous article shows how to use a systemic risk indicator to scale a hedging position and protect my premium portfolio with SPXU . ETFs are not necessarily the best hedging tools, but they are available and understandable for all investors. SPXU has the advantage to allow hedging in an account where only long positions in stocks and ETFs are possible, and without margin. Like all leveraged ETFs, it has the drawback of suffering from a decay called beta-slippage. This article calculates the real additional hedging cost incurred by this decay in 2015 for SPXU, and for another leveraged inverse S&P 500 ETF: SDS . It also shows the decay of long leveraged ETFs. What is beta-slippage? If a volatile asset goes up 25% one day and down 20% the day after, a perfect double leveraged ETF goes up 50% the first day and down 40% the second day. On the close of the second day, the underlying asset is back to its initial price. At the same time, the perfect leveraged ETF has lost 10%: (1 + 0.5) x (1 – 0.4) = 0.9 This decay is called beta-slippage. It is a mathematical property of a leveraged and frequently rebalanced portfolio (leveraged ETFs may hold futures, options and/or swap contracts). In a trending market, beta-slippage can be positive. If an asset goes up 10% two days in a row, on the second day, the asset has gone up 21%. The perfect 2x leveraged ETF is up 44%: (1 + 0.2) x (1 + 0.2) = 1.44 It is 2% better than holding the underlying leveraged 2x on margin. Beta-slippage is path-dependent. If the underlying gains 50% on day 1 and loses 33.33% on day 2, it is back to its initial value, exactly like in the first example. This time, the perfect leveraged ETF loses one third of its value, which is much worse than the 10% of the first case: (1 + 1) x (1 – 0.6667) = 0.6667 Without a formal demonstration, it shows that the higher the volatility, the higher the decay. Hence the name of beta-slippage: “beta” is the best known statistical parameter of volatility. Of course, it is uncommon to have such price variations on an ETF’s underlying asset. These numbers are here to give an amplified vision of what happens with more realistic daily returns, day after day and month after month. (click to enlarge) SPXU in red, SPY in blue. Chart and data: portfolio123 Decay of S&P 500 ETFs in 2015 The next table gives the decay of leveraged ETFs on the S&P 500 index from 1/1/2015 to 10/15/2015 (9.5 months). It was a sideways and quite volatile market, with a worse than usual beta-slippage. The decay includes beta-slippage, and also tracking errors and management fees. Ticker Return Return of SPY x leveraging factor Decay (difference) Drag on portfolio SPY -0.52% SH (1xshort) -1.84% 0.52% -2.36% -1.18% SSO (2xlong) -3.92% -1.04% -2.88% -0.96% UPRO (3xlong) -8.69% -1.56% -7.13% -1.78% SDS(2xshort) -4.84% 1.04% -5.88% -1.96% SPXU(2xshort) -9.45% 1.56% -11.01% -2.75% When using SDS or SPXU for hedging, the hedging position represents 1/3 of the total portfolio (stocks + hedge) in the first case, and 1/4 in the second one. So the real drag on the portfolio was respectively 1.96% and 2.75% compared with shorting SPY. This is the additional cost of hedging the whole portfolio during the whole period (setting it in market neutral mode), which is not the best tactic proposed in my previous article (and service ). The cost of using leveraged ETFs with any of the proposed variable hedging tactics was much lower. Rebalancing the hedge weekly also lowers the decay due to beta-slippage (but not tracking errors). Finally, the cost is lower than losing all dividends when going out of the market in a classic market-timing approach, and it is likely to provide a better long-term risk-adjusted performance. SSO and UPRO also look like decent alternatives: SSO had the lowest portfolio drag. But short selling always incurs additional risks and borrowing costs. SDS and SPXU allow to hedge without borrowing cost and with less or no margin cost. These costs depend on the broker, so the best choice for hedging with an ETF may depend on your broker. If you have the skills and possibility to manage other instruments like futures, options, CFDs, they may be more cost-effective. Keep also in mind that the hedge and the stock portfolio can be in different accounts. If you like this article, you might be interested in the next ones. Click the “Follow” tab at the top if you want to stay informed of my free-access publications on Seeking Alpha. You can even choose the “real-time” option if you want to be instantly notified.

Using Leverage To Get More Out Of Your Bond Allocation

Summary A 50/50 stocks and bonds portfolio typically generates better risk-adjusted returns than a stocks-only portfolio. This is because bond funds generate positive alpha. For an S&P 500 index fund paired with an uncorrelated bond fund, the net beta is 0.5 and the net alpha is one-half the bond fund’s alpha. An easy way to improve raw and risk-adjusted returns is to allocate one-sixth to a 3x S&P 500 fund, and five-sixths to the bond fund. The portfolio beta is still 0.5, but portfolio alpha is five-sixths rather than one-half of the bond fund’s alpha. The strategy generalizes to asset allocations other than 50/50 and allows for non-zero correlation between the bond fund and the S&P 500. Fixed Stock/Bond Portfolios Personal investors typically increase exposure to bonds as they get closer to retirement, reducing risk and drawdown potential while also sacrificing raw returns. Consider a 50% stocks, 50% bonds portfolio based on a simple S&P 500 index fund and a total bond mutual fund or ETF. The beta for such a portfolio is simply the average beta of the two funds. If there is no correlation between the two funds, the portfolio beta is 0.5. That means it tends to move 0.5% for every 1% the S&P 500 moves, which of course reduces both growth potential and drawdown potential. The portfolio alpha for a 50/50 strategy is one-half the bond fund’s alpha. So if the bond fund has positive alpha due to maturing bonds and/or falling interest rates, the portfolio will have positive alpha. This is unlike a 100% S&P 500 portfolio, which by definition has zero alpha. Notably, net positive alpha is the reason that portfolios with both stocks and bonds generally have better risk-adjusted returns than portfolios with only stocks. If bond funds didn’t generate positive alpha, you’d be better off allocating a fixed percentage to cash rather than bonds to reduce your portfolio’s beta. The same logic here applies to asset allocations other than 50/50. For example, the net alpha and beta for a 20% S&P 500, 80% total bond fund would be four-fifths the bond fund’s alpha and 0.2, respectively. Again, we are assuming zero correlation between the two funds for the moment. Fixed Stock/Bond Portfolios With Leverage A common approach to achieve a net beta of 0.5 is to allocate 50% of assets to an S&P 500 fund, and 50% to a bond fund. But we can gain a notable advantage by using a leveraged S&P 500 fund to achieve the same beta. If we used a 3x daily S&P 500 fund, we would need to allocate 16.67% of assets to the 3x fund and the remaining 83.33% to the bond fund. Our portfolio beta is still 0.5, but our portfolio alpha is now five-sixths (rather than one-half) the bond fund’s alpha. A higher alpha for the same 0.5 beta translates to better raw and risk-adjusted returns. A More General Framework Suppose you wish to achieve some target beta by combining a leveraged S&P 500 fund and a particular bond fund. Let a represent the allocation to the leveraged S&P 500 fund. This is what we want to calculate. Let b represent the bond fund’s beta. Let c represent the leveraged fund’s target multiple. Let beta represent your desired portfolio beta. The necessary allocation to the leveraged fund is given by: a = ( b eta – b ) / ( c – b ) For a concrete example, suppose we wanted to use ProShares UltraPro S&P 500 (NYSEARCA: UPRO ), a 3x daily S&P 500 ETF, and Vanguard Total Bond Market ETF (NYSEARCA: BND ), to achieve a portfolio beta of 0.75. For b , I’ll use BND’s beta since inception, which is -0.035. Our target beta is 0.75 and c is UPRO’s leverage multiple, which is 3. a = (0.75 – -0.035) / (3 – -0.035) = 0.259. So we need to allocate 25.9% of our assets to UPRO, and the remaining 74.1% to BND. By doing so, we’ll retain 74.1% of BND’s alpha (which is 0.0191%). If we had used SPY rather than UPRO, we would have retained only 24.1% of BND’s alpha. The portfolio alphas would be 0.0142% and 0.0046%, respectively. Practical Considerations The main drawback of my approach is that it requires more frequent re-balancing to maintain a target asset allocation. This translates to more trading fees and possibly more short-term capital gains taxes. Also, leveraged funds have negative alpha due to their expense ratios. For example, UPRO’s expense ratio of 0.95% translates to a daily alpha of -0.0038%. For the above example, a 25.9% allocation to UPRO would contribute an alpha of -0.00098% (25.9% of -0.0038%), which is very small compared to BND’s alpha contribution of 0.0142% (74.1% of 0.0191%). An Illustration With UPRO and BND Time to put my money where my mouth is. Let’s look at growth of $100k for various target betas achieved by combining SPY with BND, and by combining UPRO with BND. For beta of 0.1, I rebalance whenever the effective beta goes outside 0.075-0.125; for beta of 0.25, 0.2-0.3; for beta of 0.5, 0.45-0.55; for beta of 0.75, 0.7-0.8; and for beta of 0.9, 0.85-0.95. I deduct $7 for each trade (i.e. $14 per rebalance) and assume BND has a beta of -0.035 throughout. (click to enlarge) Performance metrics are given below. Table 1. Performance metrics for SPY/BND and UPRO/BND portfolios with various target betas. Beta Funds Trades Final Bal. ($1k) CAGR (%) Sharpe MDD (%) Alpha (%) 0.10 SPY/BND 3 140.7 5.6 0.116 4.2 0.00018 UPRO/BND 33 143.2 5.8 0.113 4.7 0.00019 0.25 SPY/BND 3 156.4 7.3 0.109 4.2 0.00015 UPRO/BND 35 162.7 8.0 0.110 5.1 0.00018 0.50 SPY/BND 3 183.1 10.1 0.080 8.1 0.00009 UPRO/BND 82 197.5 11.4 0.090 7.7 0.00015 0.75 SPY/BND 2 214.8 12.9 0.068 12.9 0.00005 UPRO/BND 125 237.4 14.7 0.078 12.0 0.00013 0.90 SPY/BND 0 236.7 14.6 0.064 16.9 0.00001 UPRO/BND 153 264.2 16.6 0.074 14.9 0.00011 It makes sense that we see better performance with UPRO/BND with increasing target beta. The greater the target beta, the more we have to allocate to SPY in the SPY/BND portfolio, and the less alpha we retain from the BND allocation. UPRO allows us to allocate more to BND and thus utilize more of its alpha. Risks There are some reasons for caution when trading leveraged funds. I want to briefly re-iterate similar points as in my recent article, A Simple SPY Top-Off Portfolio . If SPY has an intraday loss greater than 33.33%, you could lose your entire balance in the leveraged ETF. UPRO and other leveraged S&P 500 ETFs have historically done an excellent job achieving their target multiple, but there is no guarantee they will continue to do so going forward. In between rebalancing periods, you can suffer some irrecoverable losses due to volatility decay. I would add that the strategy presented in this article uses leveraged funds, but only to achieve a net portfolio beta somewhere between 0 and 1. In that sense, some of the concerns normally associated with leveraged funds do not apply here (e.g. extreme volatility and potentially catastrophic drawdowns). Conclusions The “bonds” part of a stocks and bonds portfolio reduces risk. But so would cash. The reason we prefer bonds is that they generate positive alpha, which improves risk-adjusted returns. Typically, a stocks and bonds portfolio utilizes only a fraction of the bond fund’s alpha. An easy way to increase that fraction is to use leverage. Historical data for UPRO and BND support the notion that using a leveraged fund in place of SPY allows you to capture more a bond fund’s alpha, thus improving both raw and risk-adjusted returns.

A Simple SPY Top-Off Portfolio

Summary A one-third UPRO, two-thirds cash portfolio mimics SPY (with some small tracking error and a net 0.32% expense ratio). Putting the two-thirds cash allocation in a short-term bond ETF like BSV allows you to recoup the 0.32% expense ratio, plus earn a little extra. Since UPRO’s inception in 2009, not including trading costs, the UPRO/BSV top-off portfolio has generated a CAGR of 15.3%, compared to SPY’s 14.3%. Going back to 1994, a 3x SPY/short-term bond portfolio has beaten SPY in 21 out of 22 years, with an average 3.1% annual outperformance. For S&P 500 investors, I see little downside to implementing a UPRO/BSV portfolio to consistently beat SPY. Background I’ve written a few articles on combining leveraged ETFs with cash or the underlying index to realize portfolios with certain properties (see for example Build Your Own Leveraged ETF ). There are a few neat things you can accomplish: Achieve any leverage between 0 and the highest multiple leveraged ETF available. Achieve a leverage multiple of an existing ETF by combining cash with a higher multiple leveraged ETF, potentially reducing your net expense ratio. Achieve net leverage of 1 by holding for example one-third of your money in a 3x leveraged ETF, and the remaining two-thirds in cash. The last point leads to the natural question: If I can mimic the SPDR S&P 500 Trust ETF ( SPY) while tying up only 33% of my available balance, why not put the remaining 67% to work in a low-risk fund that generates a few extra percentage points in growth every year? One-Third UPRO, Two-Thirds BSV The ProShares UltraPro S&P 500 ETF (NYSEARCA: UPRO ) is a leveraged ETF that aims to multiply daily S&P 500 gains by a factor of 3. It has an expense ratio of 0.95%. The Vanguard Short-Term Bond ETF (NYSEARCA: BSV ) is a short-term bond fund with an expense ratio of 0.10%. Let’s take a look at how a one-third UPRO, two-thirds BSV portfolio would have performed over these funds’ mutual lifetimes. (click to enlarge) Sure enough we get a nice little top-off with the UPRO/BSV strategy. The compound annual growth rate was 14.3% for SPY, 15.3% for UPRO/BSV rebalanced daily with no fees, and 14.8% for UPRO/BSV rebalanced whenever the effective leverage went below 0.9 or above 1.1 (with a $7 trading fee). Sharpe ratios were 0.058, 0.063, and 0.061, respectively. Of course, the greater your portfolio’s balance, the more your growth would look like the blue curve rather than the red one, since you can rebalance very frequently without trading costs hurting you very much. I know, an extra 1% isn’t that much. But just like a 1% expense ratio can really hurt you over time, a 1% boost every year can really make a big difference. If you go year by year you see that UPRO/BSV tends to tack on an extra 1-2% to SPY’s annual growth, although it doesn’t always. Annual growth of SPY and UPRO/BSV portfolios. Year SPY BSV UPRO/BSV (no fees) UPRO/BSV (fees) 2009 22.3% 2.1% 23.7% 23.4% 2010 13.1% 3.8% 15.5% 14.0% 2011 0.9% 3.0% 2.3% 2.2% 2012 14.2% 1.5% 14.9% 14.2% 2013 29.0% 0.2% 28.3% 28.1% 2014 14.6% 1.4% 14.9% 14.9% 2015 -7.1% 1.4% -6.6% -7.2% One-Third 3x Leveraged ETF, Two-Thirds VBISX We can only look at UPRO/BSV back to 2009, but it’s easy enough to switch UPRO for a hypothetical 3x SPY ETF, and switch BSV for the Vanguard Short-Term Bond Index Fund Investor Shares (MUTF: VBISX ), so we can go back further. For the 3x SPY ETF, we’ll assume no tracking error and a 0.95% annual expense ratio, mimicking UPRO. The correlation between daily gains for the simulated 3x SPY ETF and UPRO since UPRO’s inception is 0.997. The correlation between monthly gains for BSV and VBISX since BSV’s inception is 0.963. Let’s see how one-third 3x SPY, two-thirds VBISX would have performed since 1994. (click to enlarge) The top-off portfolios achieved nearly double the balance of SPY over the 20.5-year period. Sharpe ratios were 0.033 for SPY, 0.043 for 3x SPY/VBISX with no fees, and 0.043 for 3x SPY/VBISX with fees. Of course it is important to note that VBISX has done really well since 1994, with a CAGR of 4.4%. Note that the top-off portfolio with fees beat SPY in 21 out of 22 years (all except 1994), and on average beat SPY by 3.1%. You can see the consistent annual outperformance below. (click to enlarge) Another way to visualize the outperformance of the top-off portfolio relative to SPY: (click to enlarge) A Portfolio Optimization View I came to the one-third 3x SPY, two-thirds short-term bonds portfolio from the perspective of mimicking SPY by combining a 3x leveraged ETF with cash, but then putting the cash to work to gain an extra few percentage points. But you can also view the strategy from a portfolio optimization perspective. A short-term bond fund like BSV has positive alpha simply from the fact that it yields a certain small percentage annually from maturing bonds of various durations. So in periods when SPY is flat, BSV still tends to grow (i.e. it has positive alpha). Indeed if you regress monthly VBISX gains vs. monthly SPY gains going back to 1994, VBISX has alpha of 0.0036 (p < 0.001), meaning it gains on average 0.36% in months when SPY is flat. Typical Stocks/Bonds Story? It is well-known that holding both stocks and bonds tends to improve risk-adjusted returns. But if you hold an S&P 500 index fund in addition to bonds, your net beta drops below 1 and you often sacrifice raw returns. The UPRO/BSV approach is unique in that it keeps beta at 1 (assuming BSV has no correlation with SPY), while increasing both risk-adjusted and raw returns. Something like a free lunch. Upping the Ante A natural extension of the UPRO/BSV top-off strategy is combining UPRO with a longer duration bond fund. For example I like one-third UPRO, two-thirds BND, for a bigger top-off. But BND is much more variable than BSV, and also much more sensitive to rising interest rates. Another way to "up the ante" so to speak is to aim for some leverage greater than 1, say 1.25 or 1.5. You can still combine UPRO with BSV to get some extra growth at any leverage below 3, but the greater your net leverage, the greater your allocation to UPRO has to be, and the less you have left over to grow in BSV. Risks Many investors may not be comfortable with a portfolio that requires a significant allocation to a leveraged fund. Indeed, there are risks associated with leveraged funds. In particular: If SPY ever experiences an intraday loss of one-third its opening price, you could lose the entire balance in the leveraged ETF. While leveraged S&P 500 ETFs like UPRO have historically had very little tracking error, daily gains may occasionally deviate from the target multiple. In between rebalancing periods, you may suffer some irrecoverable losses due to volatility decay. It is important to note that while the top-off strategy uses leveraged ETFs, the target net leverage for the portfolio is 1. In that sense, the portfolio is not prone to the greatly amplified volatility (and potentially catastrophic drawdowns) usually associated with leveraged ETFs. It is very important to understand these issues before implementing the SPY top-off strategy. Indeed, many investors may decide that the potential for slightly higher annual returns does not justify the added risks. I personally believe that the risk/reward for the strategy is favorable. Conclusions A one-third UPRO, two-thirds BSV portfolio should behave very similarly to a 100% SPY portfolio, but often generate an extra 1-4% annual return. You'll have to monitor your effective leverage (multiply your UPRO allocation by 3) and rebalance when it deviates much from 1, but for a reasonably sized portfolio this should not detract much from your extra gains relative to SPY. Of course, you don't have to use UPRO and BSV. Other 3x S&P 500 ETFs and short-term bond funds should perform similarly. And if you want an extra boost, consider pairing the leveraged ETF with an intermediate or long-term bond fund, or a total bond fund. But your annual gains will be more variable, and you may suffer losses as interest rates rise. I am currently implementing the SPY top-off strategy with UPRO and BND, but may switch to UPRO and BSV in the near future for a more consistent, albeit smaller, bonus. Ideally, I'll beat SPY by a little bit every year, and eventually be happy.