## Monday, August 25, 2014

### Leverage Quiz

When you borrow to invest, it is called using leverage. I’ll explain the basics of leverage and then hit you with a one-question quiz to see how well you understand its effects.

If you have \$100,000 and borrow \$100,000 more so you can invest a total of \$200,000, it’s called using 2:1 leverage. If you borrowed \$200,000 to invest a total of \$300,000, that’s 3:1 leverage.

Once you’ve leveraged your portfolio, there are two ways basic approaches to maintaining that leverage. One is to rebalance periodically so that you maintain the same level of leverage. This means that if you’re leveraged 2:1 and stocks go up, you borrow to buy more shares to maintain the 2:1 leverage. If stocks go down, you sell shares and pay off some debt to get back down to 2:1. The other basic approach is to treat the debt and investments separately, just paying the loan interest. Your leverage ratio goes up and down as your investments go down and up.

If you had invested in the exchange-traded fund of Canadian stocks called XIU over the past 10 years reinvesting dividends along the way, your total return would have been +143%. With that background, here’s the question:

Q: If you had invested in XIU over the past 10 years with 5:1 leverage, rebalanced weekly and paying 4% per year interest on the loan, what would your total return have been (ignoring trading costs)?

a) +715%
b) +582%
c) +103%
d) -48%

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I grabbed some historical prices for XIU, did some spreadsheet calculations, and found the correct answer to be d) -48%. This can be hard to understand on an intuitive level. If you invest 5 times as much, why don’t you make 5 times more money? If XIU returns were so much higher than the loan interest, how could you lose money? There are many ways to answer these questions. A simple answer is that when rebalancing you are always buying more stocks when their price is up and selling when their price drops. This buying high and selling low creates a drag on returns that grows with the amount of leverage.

Another way to explain the poor results with high leverage is by explaining volatility drag. If you make 0% twice, your total return is 0%. But if you make 10% then lose 10%, you end up down 1%. Your average return is the same in each case, but the second case has a drag on returns due to volatility.

Volatility drag grows as half the square of the standard deviation of returns (per year). With no leverage, volatility drag for a stock index is usually somewhere close to 2% per year. When you leverage 5:1, you’re growing your return by a factor of 5, but you’re growing the volatility drag by a factor of 25. This makes it close to 50% per year! This huge drag overwhelms the 5 times higher returns.

You could choose not to rebalance your leverage ratio and just treat the debt separate from the investments. However, this just trades volatility drag for the possibility of a complete blow-up. If you start with \$100,000 and borrow \$400,000 more and invest the whole half-million, all it takes is a 20% investment loss to completely wipe out your original capital. If the lender demands his money back while you’re under water, you’ve lost everything and more.

All this is why leveraged hedge funds are so risky and why brokerages generally don’t permit you use more than 2:1 leverage for stocks. If you plan to borrow to invest, do so with great care.

1. “Give me a place to stand and with a lever I will move the whole world.” -Tzetzes

Pretty sure he wouldn't think this was a good idea either.

2. But there are two types of leverage - recourse where the lender has a claim on assets and nonrecourse where the lender has no claim on assets. Having some or all of the leverage as nonrecourse will affect the margin call - there never is one. Use of call or put options provide a form of nonrecourse leverage.

Also, leverage could be applied to a single part of the portfolio rather than the whole portfolio.

Finally, if the investor has some concept of valuation and has determined that value is much greater than the purchase price paid, then there is a margin of safety built into the purchase price. The risk of change in value on the downside is greatly diminished. Being built to survive a market shock is a necessity.

There are better ways to find and use leverage than the traditional house and mortgage model that the majority of investors come equipped with to the opportunities that are more widely available.

1. @Anonymous: I wonder how many investors decided that certain high-tech companies offered a margin of safety back in 2000. These investors would not have been saved by nonrecourse leverage. It doesn't much matter if there is no margin call when your portfolio stays under water indefinitely.

For all but the most savvy investors, leverage will harm portfolios in the end.

2. I think you misunderstand the concept of nonrecourse, since the cost is just the cost of the option or its imputed interest rate. There is no substantial loss of capital.

In your example of 2000, we were investing in undervalued manufacturers and distributors which had a substantial margin of safety. Tech stocks at that time were egregiously overvalued.

In today's market, there are very few undervalued companies or indices. We only have a single option (leveraged investment) that is worth the cost of the leverage.

3. @Anonymous: There are multiple ways to structure nonrecourse leverage; to do so by completely eliminating all downside risk other than the premium on options is usually disastrous for the typical investor. They make bet after bet on options that mostly expire worthless. I'll stick with my conclusion that the vast majority of investors should avoid leveraging their investments, whether they do it with house loans, simple call options, or more complex strategies that tinker with the amount of downside risk.

3. Keeping a constant leverage ratio using your proposed technique leads you to sell low (you have to sell when your portfolio tanks to reduce your leverage ratio back to desired level), and buy high (you have to buy when your portfolio soars to increase your leverage ratio back to desired level).

The solution would be to do the reverse to keep a constant leverage ratio, to buy low and sell high: When your portfolio soars, sell (but don't pay back your loan) to increase your leverage ratio back to desired level. When your portfolio tanks, buy (without borrowing money) to decrease back your leverage ratio to desired level.

The problem is that if one has the money to buy more when the portfolio tanks, why would have he borrowed in the first place? And if one sells (and doesn't pay back the loan) when the portfolio soars, what does he do with the money?

Adopting a variable leverage ratio would solve these problems, but could expose the investor to a high risk of ruin (due to possibly very high leverage ratio).

Conclusion, leverage doesn't seem such a good idea.

1. @Anonymous: Good analysis. Your idea of reacting to portfolio changes by going in the opposite direction from maintaining constant leverage reminds me of Value Averaging which suffers from the same problem: it demands that you come up with cash or take back cash when the strategy demands it as opposed to when it fits into your life.

4. The only kind of leverage I might consider is my HELOC on a paid off home. I we experience another financial crisis (40% market correction or more) at some point and talk is again of the next great depression I might consider taking out money on my Heloc in an amount less than 25% of my overall portfolio to take advantage of the potential buying opportunity. Of course prices can go lower or remain flat for decades, but the amount I would be investing suing would be modest and really just a question of moving a up a few years worth of investment contributions. That said would not invest the whole 25% at once, but instead make a series of 5% lump sums over a period of several months if valuations continued to be depressed. That said I completely agree with you on the dangers of leverage and my use of it in a future financial crisis would be modest and on a buy and hold basis only after shifting first from 80% to 100% equities. I also realize that doing so will increase the risk of behavioral errors and I have the concept included in my Investment Policy Statement. Then again I might just stand there and do nothing as John Bogle says. The nice things with a HELOC is a can make small moves without any major consequences as it is an interest only loan. Note I have zero debt and I have already maxed out all registered accounts.

1. @Anonymous: You've described many of the thoughts that ran through my head during the 2008-2009 crash. I had a paid-off home and could easily have used some leverage. In the end I chose to do nothing.

2. Thanks for the feedback. In 2008-2009 I did nothing as well. That said I had a hefty mortgage and when I made RRSP contributions I recognize that I would let money sit a few weeks as I tried to work up the courage to pull the trigger. I was over 80% equities and I know that it felt better putting new money in bonds although I did do both. That said I had not yet undergone a full conversion to passive index investing and had much less knowledge to help counter balance the media hype. The one thing I can say with some degree of confidence is that even in another major bear market any use of leverage will be modest and gradual for behavioural reasons. And prior to that step I would first gradually move by portfolio asset allocation from 85% to 100% equities.

5. Could I ask you to calculate the return on the following portfolio?

Hold XIU for the last 10 years, with 1.5:1 leverage. Rebalance monthly. Pay 4% on investment loan.

1. @Anonymous: That would have worked out well. If I modify that to weekly rebalancing (that's what the spreadsheet I created is set for), the result is +176% vs. +143% for no leverage. Of course, this ignores trading costs, but they wouldn't be too high on a large portfolio.

6. My point is that leverage can work, but excessive leverage won't. And previous comments about valuations are relevant.

Warren Buffett's leverage has been estimated at 1.6 times. His leverage isn't excessive, and he doesn't buy overpriced stocks.

This is not a blanket endorsement of leverage. Leverage is a reasonable option for the experienced investor. Notice the use of the words option and experienced.

1. @Anonymous: I have no doubt that using leverage and seeking underpriced stocks can work for some investors. However, the majority of those who try will end up with worse results than simply owning the index.

7. There is a tendency among retail investors to buy high and sell low: leverage will make this worse. So I tend to agree with you.