Leveraged ETFs

[tyates]

The ProShares ETFs and Ryder funds suffer from the Constant Leverage Trap, a problem that caused similar leveraged funds on the NASDAQ to drastically underperform in the 1990s. Here's how it works:

Proshares has $1m of investor money and borrows $1m of additional money to invest $2m in the S&P 500 index. After six months, the index appreciates 10%, and then the fund has $2.2m in assets and $1.2m of equity. (Let's ignore interest on debt for now.)

The problem is that the fund now has a lower debt to equity ratio than advertised. It is supposed to be a 2x fund, but now only has $1m of debt paired with its $1.2m of equity, making it a 1.67x fund. In order to get back to its target leverage it has to borrow $200,000 and invest in the index. Now the fund has $2.4m in assets and $1.2m in debt.

Six more months go by, and the index falls 10%. The fund now has $2.16m in assets and $1.2m in debt, leaving the investors with $960k in equity. This 4% loss surprises investors who thought that the index was down 1% for the year (+10% and -10% = -1%).

But what happens next is even worse. Because the leverage ratio is out of balance again - total assets are 2.25x the equity, not 2x - the fund has to sell its shares in order to reduce its leverage back down to 2x. It sells $240k worth of shares, and applies all of this cash to reducing the debt to $960k. The fund is now smaller than when it started.

Yes, you read that correctly, to maintain constant leverage, this index fund is constantly buying and selling, incurring short-term gains, and doing the worst possible market timing - buying more on margin when prices are high and selling when they're lower.

This is a fatal flaw in the funds, and the numbers I've used are relatively modest. Model a 15% gain in the index followed by a 20% correction and the fund implodes with a 22% loss. And this is all *before* any interest or management fees.

This is exactly what happened to the "bull" leveraged NASDAQ funds in the early 90s. The market was flat to a slightly down but volatility was high so the funds were crushed.

This "Constant Leverage Trap" is known to any finance professor, but has not been picked up by the mainstream media in the current discussion of leveraged index funds and ETFs. I should probably write an article on the topic and publish it somewhere.

Leverage can be applied to the index or any other investment, but of course the answer is to not maintain constant leverage. You start with a leverage ratio but do not adjust it as the asset value grows and shrinks.

In other words, you buy $100k of the index with 50% leverage, and if the index goes up 20% or down 20% you do nothing different. By just leaving it alone, when the index goes down you gain leverage, and when it goes up you lose leverage, which is exactly what you want. Over a period of years the investment will gain equity and lose leverage and volatility.

Most leveraged strategies also need an additional stream of cashflow or at least a cash reserve to be successful, because there will always be a point where the interest payment is due but the asset price is lower.

There is no mutual fund or ETF set up like this. Perhaps there are hedge funds, I don't know.

You can do it yourself using options and I run a site on this strategy called the Index Roll: Indexing on Steroids. It's completely non-commercial if you want to check it out. No $900 newsletters or anything stupid, no even ads, just info, tutorials, exampes, etc. My colleague and I are working on creating a fund for institutional money if we can find the right distribution partner.

Published article on the Index roll
http://etf.seekingalpha.com/article/28161

I'll also post the spreadsheet used in my analysis here:
http://indexroll.com/constant-leverage-trap.xls
You can model a +20% gain and -20% drop and see what happens to the fund... Ouch. I'll update it later to add interest payments.

Tristan
http://www.inderoll.com/ Indexing on Steroids

[pitz]

The ProShares ETFs and Ryder funds suffer from the Constant Leverage Trap, a problem that caused similar leveraged funds on the NASDAQ to drastically underperform in the 1990s. Here's how it works:

Thank you for this post; a representative of Horizons BetaPro was on ROBtv the other day (or I guess BNN) touting the activity they would have to undertake on a daily basis to maintain leverage, touting it as a positive feature of their products.

However, as you point out, there can be a nasty downside.

[sevimo]

The ProShares ETFs and Ryder funds suffer from the Constant Leverage Trap, a problem that caused similar leveraged funds on the NASDAQ to drastically underperform in the 1990s. Here's how it works:

Very interesting. One may think that 2x leveraged fund will amplify gains and losses 2x minus expenses for leverage; but it seems that it can be much worse than that. What about leveraged portfolio with constant cash inflows (i.e. individual investors who invest a portion of regular income)? I think many of those that employ leverage see constant leveraging as means of mitigating risk while keeping maximum comfortable exposure. I.e. let's assume that sell-offs do not happen (often), and all rebalancing happens by purchasing new stock, and leverage is kept constant by taking on more debt/repaying some from the cashflow.

I can see that here more money will be borrowed to buy stocks at the peak, and more cash redirected to debt repayment at the downturns (instead of buying cheap stocks). A case of buying high/not buying low...

What would be the reasonable alternative to constant leverage (without using options)?

[sevimo]

For example, do you think this LEAP is a good investment?

SPY (S&P 500 Index Fund ETF)
Market price: 145.61
Strike price: 100.00
Option price: 52.70
Expiry: 12/2009, or almost 3 years away

This LEAP gives you the opportunity to borrow $100 for 3 years for $7. That's only 2.4% interest. Does this look like a high-risk investment? Is it expensive?

If you're considering buying the Index, why not just buy the option instead, and put the $100 in a money market account? The combination is guaranteed to beat the index.

I'd say that any statement like this should trigger an alarm. Is this a good investment? I'd say yes. Is it expensive? No. Is it guaranteed to beat the index, or is it low risk? NO. There is significantly non-zero chance that you will lose everything in a severe downturn. Is it likely? Probably not, but it's FAR from guaranteed investment.

[tyates]

Sevimo, please reread... I never said the index was a guaranteed no-lose investment. Everyone knows the index has volatility.

I said to buy the 3yr LEAP call option instead of the ETF and put the balance in a money market fund. Please tell me how that combination of investments wouldn't beat the ETF itself or how you could lose all your money when 2/3 of it is in a money market fund. This isn't just my observation, it's well known that cash + low cost option beats the index.

[sevimo]

OK, perhaps I jumped to conclusions here. First of all, some people that go to options for leverage (to avoid margin requirements) overleverage themselves ridiculously; I guess this doesn't apply if you just put the rest into cash instead of more options.

Now, can you explain to me if cash + low cost option beats the index why is this not arbitraged away? Are there any funds that employ this strategy? They would be able to claim consistent index outperformance each year. Sounds too good to be true. What's the catch? I don't mean to criticize this strategy (yet ), I just didn't analyze it, but it seems unlikely that this reasoning (especially if it is well known) is not included in option valuation.

[pitz]

money when 2/3 of it is in a money market fund. This isn't just my observation, it's well known that cash + low cost option beats the index.

I normally wouldn't respond to this, but my BS detector decided to work overtime this afternoon.

Basically, if we are going to assume no leverage, you would buy the deep-in-the-money call, and then deposit an adequate amount of cash to neutralize the leverage associated with the in-the-money call.

1) The option itself has a 'cost of carry', or a time premium that is higher than the risk-free rate, minus dividends, of course.

2) The cash deposit itself will earn an amount less than the risk-free rate.

3) Options held in this fashion have to be rolled, incurring realized capital gains or losses. Interest further is implied, and not explicit, and thus cannot be written off against income. For these two reasons alone, its less efficient than a direct ETF holding.

4) The dividend tax credit is also lost under this scenario, and you incurr a bunch of commissions (and spreads) on both the investment of cash, and the purchase of the options.

5) Yes, the call provides some downside protection in extreme cases, but whens the last time you've heard of an index with earnings and dividends losing an amount that would wipe out a deep-in-the-money call? It pretty much never happens. Even the crash of 1987 wouldn't have wiped out your option.

[pitz]

OK, perhaps I jumped to conclusions here. First of all, some people that go to options for leverage (to avoid margin requirements) overleverage themselves ridiculously; I guess this doesn't apply if you just put the rest into cash instead of more options.

I basically summarized all of the options available for leverage in this thread.

Nothing at that website is any different. RRSPs are the only place where its even viable to use any of the strategies that are 'recommended' by this indexroll website.

[tyates]

Regarding your other question, you can buy at a constant leverage ratio but you'd be crazy to periodically rebalance your portfolio to maintain a leverage ratio as the market shifts. And yes, you have to use options. Margin loans are suicidal because of the high interest rates and margin call risk.

I personally am interested in leveraged index investing beacuse of the additional capital effiency - investing $70k and getting similar benefits to someone who invests $350k. But there are plenty of tradeoffs. Leveraged portfolios are not easy to exit in a downurn, for example, and have very high volatility. Still, the investing model fascinates me - the higher returns are easy calculate and I know institutional investors are very comfortable with leverage if they can diversify across investment ideas.

Honestly, leveraged investing is not for mere mortals. Leveraged investing is complex, which is why the Ryder and ProShares funds bother me so much - because there's an obvious risk there with maintaining constant leverage that they are not disclosing but is obvious to anyone who takes the hour needed to model the strategy in Excel. When these funds hit a period of volatility, they going to implode. Maybe they're imploding right now - we're in one of those periods.

[pitz]

Margin loans are suicidal because of the high interest rates and margin call risk.

5.25% is a high interest rate? Because thats what my broker charges me.

have very high volatility. Still, the investing model fascinates me - the higher returns are easy calculate and I know institutional investors are very comfortable with leverage if they can diversify across investment ideas.

Yet the 'universe' of hedge funds last year didn't even outperform the S&P500. If your strategy is so brilliant, why aren't hedge funds using it?

Honestly, leveraged investing is not for mere mortals. Leveraged investig is complex, which is why the Ryder and ProShares funds bother me so

Have a mortgage and an investment account at the same time? Thats leveraged investing .

the hour needed to model the strategy in Excel. When these funds hit a period of volatility, they going to implode. Maybe they're imploding right now - we're in one of those periods.

Yeah as I've been saying all along, funds that perform leverage internally are generally tax innefficient, for the main reason that they end up using tax-advantaged dividend income for interest expenses, instead of flowing the tax advantaged dividend income, and the tax-advantaged interest deductions out to the unitholder, as would a direct holding of an ETF would accomplish.

[sevimo]

Margin loans are suicidal because of the high interest rates and margin call risk.

5.25% is a high interest rate? Because thats what my broker charges me.

The effective rate is even less after tax refund...

[tyates]

Pitz - We can talk about Index Roll in email if you want. My topic is really about the Constant Leverage Trap. I do appreciate the feedback though.

However I am very surprised that you think that margin is superior to options. Many of your individual points are correct, but your math and conclusions are not. Let me demonstrate:

There are two investors James and Mark who both want to own the Index, specifically 100 shares of SPY, for 999 days - almost three years. James chooses Margin. Mark chooses LEAP calls. All of the examples are based on today's closing prices.

James purchases 100 shares of SPY for $14320. He uses $7160 margin and pays a 5.25% margin rate, which he offsets with the current 1.74% dividend on SPY. The difference, 3.51%, compounds over the 2.74 years and adds up to $709 additional debt, creating a total debt of $7868. He then sells the shares and pays off the debt.

Mark purchases 100 contracts on SPY with a strike price of $75 for $7090. At the end of the period, he exercises the option for $7500 and then sells the shares. (In reality of course he'd just sell the option the day before it expires.)

Note that neither investor gets dividends because James is using them to make margin interest payments, and Mark owns an option and dividend payments are baked into the premium. They both pay the same commissions, once to buy, and once to sell, so thats not in the calculation.

In order to get the same amount of shares over the same period of time, James makes two payments: $7160+$7868=$15028. Mark also makes two payments: $7090+$7500=$14590.

LEAP calls are clearly superior by $438 over the 999 day period.

We can calculate the effective interest rate of the LEAP call by doing a discounted cash flow. In order to sum the two payments and get $14320, I have to discount the second one by 1.038, which over the 2.74 years comes to a 1.2% annual interest rate. You can add back the dividend if you like and call it a 2.95% effective interest rate. That's why its cheaper to use LEAP calls - the rate is lower.

But that's not all. James also has margin call risk - if during the three year period, one one single day, SPY drops to 104, he will have to find additional cash or be sold out of his position.

I don't think most people have really studied LEAP call options, especially the deep in the money ones and would be surprised at the actual prices rather than the theory. When you look at the actual prices its hard to make the case for either margin or just buying and holding the ETF itself.

[pitz]

There are two investors James and Mark who both want to own the Index, specifically 100 shares of SPY, for 999 days - almost three years. James chooses Margin. Mark chooses LEAP calls. All of the examples are based on today's closing prices.

James purchases 100 shares of SPY for $14320. He uses $7160 margin and pays a [s]5.25%[/s]6.5%** margin rate, which he offsets with the current 1.74% dividend on SPY. The difference, 3.51%, compounds over the 2.74 years and adds up to $709 additional debt, creating a total debt of $7868. He then sells the shares and pays off the debt.

** note: since we are talking US dollars here, I inserted the USD rate for margin at my broker

Actually, you need to deduct the effect of income tax on the net of the interest expense and the dividends. So 6.5% - 1.74% = 4.76%. In a 35% tax bracket, the after-tax interest expense is 3.1%.

The implied carry in the options is equal to roughly 5.25% - 1.74% * (1-35%/2) = 2.9%.

So far, the options are winning.

Mark purchases 100 contracts on SPY with a strike price of $75 for $7090. At the end of the period, he exercises the option for $7500 and then sells the shares. (In reality of course he'd just sell the option the day before it expires.)

And gets hit with a capital gains liability. Over the span of 3 years, the time value of money will have a very minimal impact on the value of deferred capital gains. A long-term (20+ year) hold of SPY should yield an effective long-term capital gains tax rate, annualized, of approximately 8%. A short term hold of SPY or its options will yield a capital gains tax rate approaching 17.5%, in other words, one-half the marginal rate on income.

This spread can be substantial. If SPY earns 10%/year, 8% taxation reduces the return to 9.2%/annum, but if you're incurring capital gains each year, the return will be reduced to 8.25%/annum. The loss of 100bp of annual return far outweighs the 20 basis points of interest expense savings as calculated previously.

Note that neither investor gets dividends because James is using them to make margin interest payments, and Mark owns an option and dividend payments are baked into the premium. They both pay the same

In the Canadian-source dividend context, you lose the benefit of the dividend tax credit. This tax rate differential makes flipping options even less attractive, as the rate of taxation on dividends, in most cases, is now lower than that of capital gains, even lower than the rate on long-term deferred capital gains.

commissions, once to buy, and once to sell, so thats not in the calculation.

If this is a short-term trade, sure. But why not take a longer-term view?

In order to get the same amount of shares over the same period of time, James makes two payments: $7160+$7868=$15028. Mark also makes two payments: $7090+$7500=$14590.

LEAP calls are clearly superior by $438 over the 999 day period.

But theres no interest deduction, and you end up locking in a realized capital gain after a couple years. As the above has demonstrated, this is less efficient than writing off (more expensive) margin interest, and deferring capital gains on a long-term basis.

you like and call it a 2.95% effective interest rate. That's why its cheaper to use LEAP calls - the rate is lower.

Sure, but you are ignoring taxes.

I don't think most people have really studied LEAP call options, especially the deep in the money ones and would be surprised at the actual prices rather than the theory. When you look at the actual prices its hard to make the case for either margin or just buying and holding the ETF itself.

Inside the RRSP, definitely. But outside, doing the deferred capital gains 'thing' provides an extra 0.8% return just based on taxes alone.

Oh yeah, and did I mention that the margin investor doesn't have to pay any commissions whatsoever once the trade has been initiated? The margin investor benefits from the use of shorter-term interest rates being used as the benchmark instead of the 2 or 3 year rate*. The margin investor isn't hit with huge spreads buying/selling options. The margin investor also receives the benefit of rising dividends, while the option buyer receives no dividends whatsoever.

* -- historically the yield curve hasn't been inverted, and 2 or 3 year money has carried a risk premium associated with interest rate risk, in addition to other risk premiums applied over the risk-free rate.

[tyates]

I won't go into all the tax math but there are some things that make your calculations incorrect:

1. Margin interest can only be deducted against investment income. Your calculations assume you have a pile of high-tax short-term gains that you want to deduct against. If you're a buy and hold investor though, why do you have all these gains? Most people most of the time will probably be deducting most of their margin interest against qualified dividends or long-term gains, which are taxed at the 15% rate. Therefore your benefit from paying margin interest will be significantly lower than you project.

2. Any security, whether it is a stock or a LEAP call, that is held for more than one year will get LT capital gains treatment. You seem to be under the impression that options are always short-term. That's not true at all. You may be confusing an option on an Index ETF with an Index Option, which is taxed at 60% ST rate, 40% LT rate. Equity options get ST or LT rates, non-equity options get the blended rate.

3. You also mention additional transactions, commissions, etc. I only count two $5 transactions in three years for the LEAP call in the example. You were correct that I did forget the spread. I can't get that after hours but I don't think its more than 30 cents a share.

I won't get into the LT view here (over 3 years) because its a complex topic, but I'll just say that the cost to extend a deep in-the-money option is extremely low and can actually go below zero at some points. You can model this in an options calculator by comparing the same deep-in-the-money option and varying the expiry date - or just look at the spread between the 1/08 and 1/09 @30 call options on a high-dividend stock like Bank of America. Same principle.

4. There wasn't any discussion of the very serious risk of margin call. A portfolio held with a significant level of margin has a built in bomb that could go off anytime. If an earthquake in California hits and the market crashes, I don't want to have to worry about my retirement portfolio being liquidated and sold out from under me.

I would be happy to concede that the financial difference between a LEAP call and a margin loan is not that big for an investor with a low margin rate and a high tax rate. Still, even if the financial picture was equal - and options still seem somewhat cheaper to me - the fact that you can choose your own leverage ratio and change it over time without risk of margin calls makes options the clear winner for a long-term investor who wants additional leverage.

[pitz]

I won't go into all the tax math but there are some things that make your calculations incorrect:

1. Margin interest can only be deducted against investment income. Your calculations assume you have a pile of high-tax short-term gains that you

In Canada, not true. Margin interest can also be deducted against all other income including employment income for the purposes of Canadian taxation.

2. Any security, whether it is a stock or a LEAP call, that is held for more than one year will get LT capital gains treatment. You seem to be under the impression that options are always short-term. That's not true at all. You may be confusing an option on an Index ETF with an Index Option, which is taxed at 60% ST rate, 40% LT rate. Equity options get ST or LT rates, non-equity options get the blended rate.

In Canada, capital gains are capital gains. We do not distinguish between short term and long term gains. Our taxation authorities can only require less preferential 'income' treatment of capital gains only if a taxpayer's investment activity is deemed a 'business' or an 'adventure in the nature of trade' (ie: a daytrader). Alternatively a taxpayer may file an irrevocable declaration with the authorities for income treatment of investments, but this is usually ill-advised.

4. There wasn't any discussion of the very serious risk of margin call. A portfolio held with a significant level of margin has a built in bomb that could go off anytime. If an earthquake in California hits and the market crashes, I don't want to have to worry about my retirement portfolio being liquidated and sold out from under me.

So spend $40 on some $100 SPY puts. Still cheaper than sacrificing 80bp/year of return.

I would be happy to concede that the financial difference between a LEAP call and a margin loan is not that big for an investor with a low margin rate and a high tax rate. Still, even if the financial picture was equal - and options still seem somewhat cheaper to me - the fact that you can choose your own leverage ratio and change it over time without risk of margin calls makes options the clear winner for a long-term investor who wants additional leverage.

Under the US tax system, I can accept that. Under the Canadian system, I believe margin still is less expensive.

So I guess we're both right

[tyates]

Agreed... actually this is really helpful because I've been trying to find out how this type of scenario would works in other countries or for international investors. I have a Yahoo Answers question on the same topic but haven't gotten any feedback.

There's also another problem related to financial leverage which I alluded to earlier but maybe you could help me with. It's on topic as it's the same problem faced by ProShares.

For simplicity, let's say that you're investing in an index that returns 10% with 50% leverage and a 5% rate of interest. Your expected annual return is 15%.

However, can you really grow your portfolio at a 15% rate? Because the index is unpredictable you can't assume at the end of every year that you can sell your portfolio for 15% more and then reinvest the same way and get the same return next year.

If we apply a standard volatility of 15% to our 50% leveraged portfolio we get some big spreads. 1 standard deviation is -15% to +45%, 2 std dev is -45% to +75%. There's nowhere near enough reliability there to regularly sell appreciated shares and reinvest, and in extreme market conditions you can't even sell shares to pay your interest.

So how do you create a reinvestment strategy that takes advantage of the superior average appreciation of the leveraged index? Obviously the constant leverage strategy is the worst one you can think of. So what's the best one?

One solution is to never lever after your initial purchase, and to basically let time raise the price of the asset which reduces your overall leverage. However this isn't really re-investing gains - just buying and holding indefinitely. And you have to pay the interest out of pocket.

I think the solution may be to set up a regular investment schedule and use time as your buy and sell trigger. In other words, buy your portfolio monthly over four years and then hold each share for four years. Then sell those shares and buy slightly more shares back at the original level of leverage. Keep any extra money in cash for future interest payments, purchases, etc.

This would work even in an extended multi-year downturn, however using random stock prices, a model will eventually generate a series of stock returns in which you run out of cash, so there's some luck involved. (Imagine the stock price rising sharply for four years and then falling heavily for four years.)

I've also done models where you sell and rebuy 20% of your shares in 2yrs, 20% in 3 yrs, 20% in 4 yrs, etc. You still have to control the rate of investment growth. I haven't done the model with multiple correlated indexes like the SPY, MDY, IWM, etc, maybe that's my next project.

Any ideas? If I do write about the perils of the Constant Leverage Trap, then I should have an alternative re-investment strategy - though actually even no reinvestment at all is superior.

[pitz]

Agreed... actually this is really helpful because I've been trying to find out how this type of scenario would works in other countries or for international investors. I have a Yahoo Answers question on the same topic but haven't gotten any feedback.

Yeah tax policy can be unpredictable. In Canada, a political party has actually promised 'relief from capital gains if the investment proceeds are re-invested within 6 months'. This would mean that futures and/or options could be rolled without the taxation concerns that I presented earlier.

And of course, dividend taxation policy changes on both sides of the border. For instance, tax policy enacted by the United States in the wake of the 2001 economic collapse lowered dividend taxation rates substantially on certain dividends. Substantial reductions in dividend taxation have also taken place in Canada recently, specifically to encourage companies to pay out more dividends.

For simplicity, let's say that you're investing in an index that returns 10% with 50% leverage and a 5% rate of interest. Your expected annual return is 15%.

However, can you really grow your portfolio at a 15% rate? Because the index is unpredictable you can't assume at the end of every year that you can sell your portfolio for 15% more and then reinvest the same way and get the same return next year.

If the underlying corporations are optimizing their use of debt, in relation to the amount of capitalization in the overall firm, then I would suggest that adding additional leverage will not, in the long term, create additional value for the investor and probably will end up destroying value.

The question really becomes, can an individual investor counteract excess balance sheet liquidity carried by the firms that they are invested in? (effectively outguessing corporate management in the allocation of liquidity?) For instance, balance sheet liquidity of S&P500 firms is at all-time high which means that a lot of cash is being retained within corporations. I believe if you can time your use of leverage to be counter-cyclical to the accumulation of cash on corporate balance sheets, you can capture additional value that is not being captured by the corporations themselves.

Of course, maybe 'corporate america' knows something about the future economy that we, as individual investors do not, and are thus hoarding liquidity to prepare for such an event. I mean, the amount of cash sitting on balance sheets is absolutely crazy, while there is a significant amount of evidence that productivity and fixed investment has slowed precipitously. Personally I feel S&P500 CEO's are a bit too gun-shy -- too much capacity was built leading up to the crash of 2000, so now they are being overly cautious in building new capacity. You see it in many sectors, for instance, big oil is adding most of its new reserves through M&A, rather than actual exploration programs. Much of the technology sector has stopped R&D altogether, etc.

If we apply a standard volatility of 15% to our 50% leveraged portfolio we get some big spreads. 1 standard deviation is -15% to +45%, 2 std dev is -45% to +75%. There's nowhere near enough reliability there to regularly sell appreciated shares and reinvest, and in extreme market conditions you can't even sell shares to pay your interest.

Excess balance sheet liquidity tends to lead to periods where, historically speaking, firms experience lower overall market volatility. Stock buybacks provide a 'floor' price, and 'leveraged buyout' firms are willing to roll the dice on firms that become irrationally undervalued by the market, creating, once again, a floor under prices.

A lack of firm balance sheet liquidity does exactly the opposite.

So how do you create a reinvestment strategy that takes advantage of the superior average appreciation of the leveraged index? Obviously the constant leverage strategy is the worst one you can think of. So what's the best one?

I think you need to dig deep onto the balance sheets of the underlying to judge how much volatility can reasonably be expected in addition to macroeconomic trends. I don't think you can just look at a stock charts alone to make that determination.

One solution is to never lever after your initial purchase, and to basically let time raise the price of the asset which reduces your overall leverage. However this isn't really re-investing gains - just buying and holding indefinitely. And you have to pay the interest out of pocket.

Eventually the portfolio return will trend towards the unlevered return. Not a bad idea, IMHO, for a young investor who is looking to reduce risk over time. Leverage to the hilt in one's 20s, and reduce into one's 30s, 40s, and 50s. Start buying fixed income in one's 50s.

Sounds like pretty much what happens with home-buyers. Leverage is maximized initially, but that loan is eventually paid off, and the majority of (Canadian) homeowners do not take out new mortgages against paid-off houses. We don't have a crazy re-financing industry here -- most home equity extraction that takes place in Canada are done through HELOCs at prime of 6% (risk free rate + 1.75%), and not lump-sum long term refinancings as are traditionally found in the US (where HELOCs are substantially more expensive).

I think the solution may be to set up a regular investment schedule and use time as your buy and sell trigger. In other words, buy your portfolio monthly over four years and then hold each share for four years. Then sell those shares and buy slightly more shares back at the original level of leverage. Keep any extra money in cash for future interest payments, purchases, etc.

Don't know what this algorthm would do, aside from causing more churn and cap gains tax than necessary.

Any ideas? If I do write about the perils of the Constant Leverage Trap, then I should have an alternative re-investment strategy - though actually even no reinvestment at all is superior.

I am a big believer in the consolidated balance sheet approach, as I sort of described above, where you consolidate the balance sheets of your investments, with your own balance sheet, and then determine an appropriate amount of leverage given the underlying financial conditions of the firms you are invested in, paying particular attention to liquidity. Of course, the portolio still has to be able to withstand a random event such as the 1987 crash, but you mostly could have avoided the 1973 crash, the 2001/2002 crash, and the 1929 crashes (all of which would have destroyed leveraged portfolios), simply by being mindful that problems on corporate balance sheets will eventually migrate to your own, (but not necessarily vice versa).

Of course, another factor to consider is the benefits of a potential margin call. I know when the markets collapsed in 2001/2002, I scrimped and saved every penny and threw it into the market because I was confident that it would roar back (the collapse in Canada was pretty irrational, IMHO, because Canada's economy barely even weakened in the wake of the Sept. 11 attacks or even SARS for that matter). At the top of the market (ie: recently), I've been more of a big spender because I perceive the marginal utility of saving my excess dollars and throwing it into more stock is less than it was when the market was substantially 'cheaper'. This behaviour can contribute positively to returns as well. The deflation associated with the 2001/2002 collapse was also very helpful in saving a lot of money, as many of my costly expenses (particularly travel) fell dramatically in price. ($1 coast-to-coast flights on Canada's national airline were very nice circa 2002, lol, and you'd still get the whole row to yourself)

[sevimo]

Of course, another factor to consider is the benefits of a potential margin call. I know when the markets collapsed in 2001/2002, I scrimped and saved every penny and threw it into the market because I was confident that it would roar back

I'd say pro and cons of leverage is nothing compared with investing discipline

[adrian2]

Yes, the call provides some downside protection in extreme cases, but whens the last time you've heard of an index with earnings and dividends losing an amount that would wipe out a deep-in-the-money call? It pretty much never happens. Even the crash of 1987 wouldn't have wiped out your option.

To paraphrase, I normally wouldn't respond to this, but my BS detector decided to work overtime this morning .

Pretty much never happens? Depends how deep is deep-in-the-money. Japanese stocks lost 80% in the early 90's. UK stocks lost around two thirds in the mid 80's. US stocks lost a lot in the Great Depression. I won't refer to other countries since the above are/were the top 3 market caps in the world.

[sevimo]

I am a big believer in the consolidated balance sheet approach, as I sort of described above, where you consolidate the balance sheets of your investments, with your own balance sheet, and then determine an appropriate amount of leverage given the underlying financial conditions of the firms you are invested in, paying particular attention to liquidity.

It makes sense, but does it really work for indexing? It's one thing to go through balance sheets if you keep several individual stocks, but what if I invest in Wilshire 5000? Or can I see somewhere consolidated balance sheets for indexed baskets like VTI?

[pitz]

It makes sense, but does it really work for indexing? It's one thing to go through balance sheets if you keep several individual stocks, but what if I invest in Wilshire 5000? Or can I see somewhere consolidated balance sheets for indexed baskets like VTI?

There was a thread where someone pasted a chart of the long-term 'current' ratios of corporations. Basically, the overall liquidity of the S&P500 bottomed out in 2001, and has been climbing ever since. A similar pattern repeated itself through various stages of the market in the past 30-40 years, but consistently, one pattern emerged -- high levels of liquidity are usually a precursor to a substantial multi-year rally in the indicies, and low levels of liquidity are the opposite.

I think you could fairly safely use the S&P500 figures as a proxy for VTI or the Wilshire 5000, as those indicies are fairly correlated with the S&P500 anyways.

[sevimo]

There was a thread where someone pasted a chart of the long-term 'current' ratios of corporations. Basically, the overall liquidity of the S&P500 bottomed out in 2001, and has been climbing ever since.

All I can find are discussions of P/E ratios of indices, but I guess that's not what you're talking about. I must be using wrong keywords in the search

[tyates]

Sorry for the delay - I think this board was down. This is a very early draft of the article I'm thinking of writing on the constant value trap tht exists with the ProShares ETF, Ryder leveraged funds, and other leveraged index funds.

In order to maintain constant leverage, a leveraged index fund has to buy shares when prices rise, and sell when the market falls. Intuition says that this is likely a bad strategy, amounting to buying high and selling low, and backtesting using historical data confirms these suspicions.

We downloaded the available historical pricing data for the SPY ETF and ran it through a model in which the fund buys and sells shares in order to maintain a constant leverage ratio of 2. No interest is calculated at first – the object is simply to see the results are of buying when the market is up and selling when the market is down.

In the model, the fund started with 10,000 shares of SPY in Jan 1993 and bought additional shares during the bull market of the 1990s, finally arriving at over 32,000 shares in Jan 2000. Then, during the downturn the fund has to start selling shares to maintain a constant leverage ratio, liquidating almost 16,000 shares during the next three years. 2,400 shares were sold just in the market week after 9/11/2001.

What’s interesting is that the constant leverage trap does make the fund sell huge amounts of shares in a downturn, but also just prevents it from ever blowing up. The fund will always have some shares left, even if it’s just a small fraction of the original total.

The most important question for a long-term investor is whether the fund significantly beats the index. The answer is yes, to some extent, if you pick the right starting year.

When interest payments are added to the model using a cost of debt of 5%, the fund still bought heavily during the bull run and sold during the bear market, but also continually liquidated shares to pay interest. In terms of performance, during a fourteen year period the fund beat the S&P 500 by 34%.

But this outperformance is largely a function of the starting year. A fund investor who bought at the beginning of 1993, 1994, 1995, or 2003 would have beat the index by about 30 points over the period. Unfortunately an investor who bought in 1998, 1999, 2000, or 2001 would have underperformed by 30 points. And anyone that invested in the other years would have matched the index, give or take about ten percent.

The volatility was very high. In the best year, the fund gained 81% and in the worst year it lost 43%.

Now this could be seen as a repudiation of leveraged investing – but that would be drawing the wrong conclusions.

If the fund simply never bought or sold any additional shares after the original 1993 investment, the investor would have 6% more money, and a lot less short-term gains, transactions, and a lot loss volatility. It’s clear that a reinvestment strategy based on maintaining constant leverage doesn’t add any value based on historical data – it actually reduces it.

Of course, if a fund doesn’t buy any additional shares its leverage will reduce over time. In the model the fund's leverage falls from 2x to 1.2x over the 14 year period. Still, this may be exactly what an investor wants as they get closer to retirement.

Is it possible to maintain a degree of leverage over time and get a long term performance benefit? We then built a model in which the fund very slowly and steadily increases the number of index shares by about 3% a year, using simple dollar cost averaging to buy more shares when prices fall and fewer shares when prices rise.

This model allowed the fund to avoid accumulating as many shares during the upturn, and then to accelerate its purchases during the bear market. The leverage ratio, initially 2x, falls to 1.3x at the height of the bull market, and then rises to 1.8 at the end of the bear market. We take on more leverage as the market gets cheaper, which boosts our future returns.

Over a ten-year period, 1997 to 2006, $1 invested in the DCA Leverage fund would be worth $2.47, as compared to $2.19 for the index fund, and $2.04 for the Constant Leverage Fund. Investments made in individual years perform well also, beating the index in ten of the fourteen years, but the advantages become more apparent over longer holding periods.

The most important benefit of the DCA leverage strategy is that it saves investors from financial suicide if they happen to invest in January 2000, just about the top of the market.

During the next three years, the index loses 33%, the DCA leverage fund loses 50%, and the Constant Leverage Fund loses 68%. The index then recovers its losses over three years, the DCA leverage fund recovers over four years, and the Constant Leverage Fund would not have recovered at all – maybe it will in a few more years.

Note that I am not advocating this specific dollar cost averaging investing model for investors, but simply showing that it is possible to use leverage and simple regular reinvestment strategies to create value rather than to destroy it like the Constant Leverage Trap does.

I understand why companies like ProShares and Ryder are maintaining constant leverage – because they want to market their fund in a specific way, as a tool that investors can use for capturing daily appreciation.

However, I don't think that the risks of holding these funds for longer periods are well disclosed. Investors don't expect to lose two-thirds of their portfolio during a down market similar to the one we experienced recently, resulting in a ten-year performance that's actually inferior to the index it tracks.

As of now, even though models clearly show that there are benefits to using leverage in index-based portfolios held for long periods of time, there is still no practical solution for investors. Currently, their only choices are to use margin, rolled Index Options, or rolled Index ETF LEAP call options. However, using margin creates margin call risk of course, and option mechanics are not generally well understood, making costly mistakes easy.

Perhaps a company will offer a leveraged fund or ETF at some point that does not use constant leverage, but instead uses a better re-investment solution such as dollar-cost averaging. If the fund also had the ability to borrow cheaply and could manage the leverage ratio well, it would provide considerable value to long-term investors.

Exhibit 1:

Performance Comparisons

Indexing Strategy 5yrs 10yrs 14yrs 1/2000-12/2002
Buy & hold index +32.7% +119.5% +306.1% -33.1%
Maintain 2x constant leverage +20.3% +103.5% +447.0% -67.2%
50% initial leverage, pay interest, no additional purchases +32.5% +140.7% +479.0% -41.2%
50% initial leverage, pay interest, grow portfolio 3% a year through debt +36.1% +147.0% +518.6% -49.8%

Note: The entire model with all of the data and calculations used in this article can be downloaded at:

http://www.indexroll.com/backtested-con ... verage.xls

[pitz]

Try running this algorithm:

BUY INDEX (2X leverage) when 12-month trailing P/E < 1/(10-year T-bond rate) + k
SELL INDEX down to 1X leverage (ie: no leverage) when 12-month trailing P/E > 1/(10-year T-bond rate) + k

for k=-5, -4, ... 0, +1, +2 ...+5

If you have the datasets available.

Thanks. I think that the implementation of this algorithm could increase returns while reducing overall leveraged portfolio volatility over a similar interval, and prevent the dillema of investing in, for instance, the Nasdaq or the Nikkei, at its peaks.

edit: also interest deductibility, at least in Canada, would improve the results further. Another useful technique to mitigate volatility, at least psychologically, would be to mark the accrued tax liability to market alongside that of the fund's gains as well. Clips the gains, but also clips the losses, and makes the whole thing easier to digest for the leveraged investor.

[adrian2]

Very interesting analysis, tyates, thank you.

I've always wondered how the bear funds (e.g. Rydex Ursa) manage to maintain a negative correlation to the index, without running down to zero as the index rises. Your message above explains how.