Quantitative Trading:Leveraging the Permanent Portfolio using the Kelly Formula?

[blackomen]

I'm studying Quant Trading and the idea of using the Kelly Criteria to determine how much to leverage a portfolio.  (See: http://epchan.blogspot.com/2006/10/how- ... u-use.html )  This formula calculates the most optimal amount of leverage for a portfolio to grow steadily..

I'll cut out the theory and the mathematical derivations but I'll summarize the formula as follows:

f = (m-r)/(s*s)

m = expected return of the strategy.
r = interest rate on margin (from your broker.)
s = standard deviation of your returns

result: f = how much leverage you should use.

Let's say the permanent portfolio returns an average of 9% a year, your broker charges 7% on margin (that's what you get at Zecco.)  The standard deviation of your returns is 5% (I got a similar # when I actually backtested my version of the permanent portfolio.)

Plugging in those numbers:  (0.09-0.07)/(0.05*0.05) = 8.0 -> you should leverage the permanent portfolio 8 times! (Of course, not many brokers offer that much leverage on stocks and ETFs so you'd need to use futures to get that much leverage.)

Let's compare that with a portfolio that's long just SPY (S&P 500 ETF):

Expected return: 9.35%
Standard deviation of returns: 21.92%

Kelly leverage for SPY = (0.0935 - 0.07)/(0.2192*0.2192) = 0.489

That means you should only invest half of your money in SPY if you intend to buy that ETF and no other investments!

I'm just curious if anyone has tried to leverage the Permanent Portfolio for a long period of time.  The risk to reward is so much better than the vast majority of investments or even portfolios managed by professionals, so it's very tempting for me to add some leverage to increase my returns without putting myself at great risk of financial ruin.

Since Harry Browne didn't like leverage, is this a crazy idea?  I probably won't go 8x leverage..  I'm already at 3x leverage and up about 10-15% on the year after starting the permanent portfolio in August 2011.

[beafet]

I would think the issue is "m". A key appeal of the PP strategy is no one knows what the future holds.

[MediumTex]

I would stay away from leverage with the PP.

Maybe treat the leveraged portion of your PP as your VP.

[clacy]

Keep in mind, that there have been plenty of quant funds that have went kaput, using leverage formulas on various portfolios over the years.

[craigr]

Since Harry Browne didn't like leverage, is this a crazy idea?  I probably won't go 8x leverage..  I'm already at 3x leverage and up about 10-15% on the year after starting the permanent portfolio in August 2011.

The fastest way I've seen people lose everything they have in investing is by using leverage.

Here is my standard question on investing with borrowed money:

If investing on leverage was such a great idea, then why are the brokerages willing to loan you money at 7% when they could just invest it themselves and pull in the big bucks?

[craigr]

Also I will say that the markets cannot be modeled with mathematical formulas so simply. Markets are a chaotic system and too many unpredictable variables are in play. Plenty of very smart quants have been badly burned going down this route.

[blackomen]

I would stay away from leverage with the PP.

Maybe treat the leveraged portion of your PP as your VP.

I'm not really investing using "Permanent Portfolio" as my core strategy..  just stealing some ideas from PP...

[blackomen]

Since Harry Browne didn't like leverage, is this a crazy idea?  I probably won't go 8x leverage..  I'm already at 3x leverage and up about 10-15% on the year after starting the permanent portfolio in August 2011.

The fastest way I've seen people lose everything they have in investing is by using leverage.

Here is my standard question on investing with borrowed money:

If investing on leverage was such a great idea, then why are the brokerages willing to loan you money at 7% when they could just invest it themselves and pull in the big bucks?

Also, many brokerages make money by trading against their clients..  offering margin will attract the more aggressive risk takers.  The average retail investor is not gonna be using the permanent portfolio and will probably make poor decisions when they're under pressure, when their plans don't unfold, when they lose too much money too fast, etc. and make good candidates for the broker to "fade".

[stone]

I suppose the formula has inbuilt assumptions about how to extrapolate what the chances are of a meltdown event given the standard deviation. Its well documented  that supposed "three sigma events" actually happen quite often in real markets. The distributions are way off a normal distribution.

Also, how can you leverage cash? Do you use some derivative that increases in value in relation to the short term interest rate? I wonder whether one of those USDbull index etfs might be a leverageable thing for the cash part?

For me the PP itself is quite risky enough. You only need to multiply any number by zero once to get zero.

[AdamA]

Also I will say that the markets cannot be modeled with mathematical formulas so simply. Markets are a chaotic system and too many unpredictable variables are in play. Plenty of very smart quants have been badly burned going down this route.

Has anyone seen the movie Margin Call?

[Ad Orientem]

Granting that it is possible to buy so called leveraged ETFs that do not leave you personally exposed to the possibility of a margin call, I am still not a fan of it.  You really would need steady nerves and a willingness to potentially incur very steep losses.  And it goes without saying that this would only be appropriate in a VP.  But honestly, "leverage" is a word that just instantly turns me off to almost any investment suggestion.  Once I hit that word I tend to stop paying attention.

[blackomen]

I suppose the formula has inbuilt assumptions about how to extrapolate what the chances are of a meltdown event given the standard deviation. Its well documented  that supposed "three sigma events" actually happen quite often in real markets. The distributions are way off a normal distribution.

Also, how can you leverage cash? Do you use some derivative that increases in value in relation to the short term interest rate? I wonder whether one of those USDbull index etfs might be a leverageable thing for the cash part?

For me the PP itself is quite risky enough. You only need to multiply any number by zero once to get zero.

I buy UUP in lieu of the 25% cash..  depending on your definition of "permanent portfolio", what I'm doing may not qualify as "permanent portfolio" in the strictest sense.

25% GLD
25% SPY
25% TLT
25% UUP

[AdamA]

I buy UUP in lieu of the 25% cash.

Why?

[stone]

Adam, I had also supposed that a USD bull etf like UUP would be what would be used as "cash" for leveraging up. In a liquidation panic, people with leveraged holdings are going to try and sell off everything to get USD to pay the margin calls. That will give a strong USD or so the story goes. I suppose though that Yen might actually get an even bigger effect in that way than USD does. It might be safer to have both a Yen bull etf and the USD bull etf. If rather than a fleeting 2008 style liquidation panic; you instead get faced with a hike in USD short term interest rates, then the USD bull etf would also save you from a 1981 style PP synchronised fall so long as all the other currencies did not simultaneously decide to raise rate (which of course they might do). Raising rates for the USD but not Yen would make a Yen etf a liability.

What is the tracking error like for UUP at those critical moments when you need it most? It is all very well having great tracking acuracy for the 99.9% of the time when it is just a drag on the portfolio. What matters is the lack of tracking error for the darkest hour when the margin calls come in for the rest of the portfolio. Presumably some other UUP holders have bought it for the same reason. They are going to be selling it hand over fist inorder to get cash to pay their margin calls. Might some more direct holding such as USD futures be less exposed to traking error risk.

I have to stress that I have no personal temptation to get involved in any of this but I do think it poses the greatest risk out there for those of us who hold unleveraged PP. The more leveraged PP there are, the more margin calls are going to make the whole PP plumet in unison. I think that allready happens to some extent. It makes adding to the PP on such days worth waiting for I guess.
I guess that new PP etf is going to be held on margin by lots of people. It might cause the end of the party for the PP strategy???

[blackomen]

What is the tracking error like for UUP at those critical moments when you need it most? It is all very well having great tracking acuracy for the 99.9% of the time when it is just a drag on the portfolio. What matters is the lack of tracking error for the darkest hour when the margin calls come in for the rest of the portfolio. Presumably some other UUP holders have bought it for the same reason. They are going to be selling it hand over fist inorder to get cash to pay their margin calls. Might some more direct holding such as USD futures be less exposed to traking error risk.

Maybe buy calls on UUP instead of holding the underlying?  During those "darkest hours", whether or not the tracking error is great, it's likely the implied volatility will be elevated.

[stone]

blackomen, I'd still be very spooked that the entire account would dip to below zero momentarily, you'd have to sell up and end up owing money. Perhaps a week later the holding would have rebounded strongly but for you that is too late. I suppose it takes a certain amount of time for various price effects to filter through the system. Call options on UUP might just be adding an extra tier of time delay?

[akratic]

1) No one bets full kelly for a number of reasons
1a) Betting half kelly cuts your volatility significantly but still gives you 75% of the returns
1b) Betting full kelly leaves you in great danger of overbetting if any of your assumptions are incorrect, and overbetting is disastrous: returns go down and volatility goes up.  Remember that betting 2x kelly has an expected return of ZERO, and anything above 2x kelly and you're on your way to bankrupt.

2) As pointed out, normal distributions are poor fits for financial returns due to kurtosis and fait tails, etc

3) Only a 5% stdev for the PP is rather optimistic.  Here's the daily stdevs for your UUP PP for all the years that UUP has existed: 6.9%, 9.0%, 8.0%, 6.4%, 7.1%.

Suppose you used an 8.0% stdev assumption and half kelly bets:

0.5 * (0.09 - 0.07) / (0.08 * 0.08) => 1.56 leverage, which seems a bit more reasonable

Suppose you stick with the assumption of a 9.0% mean and a 5.0% stdev and full kelly bet, giving you an f* of 8.0.  If the future unfolds such that the optimal f* was below 4.0, your expected returns are negative.  In other words, my 9% return, 7% margin, 8% stdev example (=> f* of 3.12) leaves you expecting to lose money and your bankroll.

Let me say that another way to make sure it sinks in.  With 8x leverage, 7% margin, 9% average returns, and an 8% st dev, if you could make that bet infinite times, the Kelly Formula tells you that in the long term you would expect to be completely bankrupt.

I guess what this comes down to is: how certain are you about getting 9% returns with 5% stdev in the future?

[MediumTex]

Another idea to keep in mind is that leverage is normally an expression of maximum optimism in a certain approach to investing.

We know from history that periods of maximum optimism are often followed by periods of sub-par performance. 

If too many people start talking about using leverage with the PP, I would anticipate a period of PP returns that are below interest rates on margin debt.  That just seems to be how reality deals with such things.

[Kel]

As I recall the Kelly Criteria was what Larry Williams used in the Robbin's Trading Championship to take his futures account from it's starting equity of $10,000 and increase it by 11,376%  in 1987.
http://www.robbinstrading.com/worldcup/standings.asp

Ralph Vince in his book The Mathematics of Money Management discusses this strategy. Ralph worked with Larry Williams prior or at the time he was using this methodology for the contest. As I recall it sort of gave rise to fixed factional trading and Vince wrote about that as well..  Since I come from a futures trading background - I have run some hypotheticals on historical data - for fixed fraction positioning- big drawdowns and ups are part of that and of course always a risk of blowing your account too. In fact as I recall Vince used the analogy that if the only way you could die is by being hit by lightening - sooner or latter you'd be hit by lighting...i.e. sooner or latter you blow your account so he suggested you pick a reasonable target and use the strategy until you blowout or reach the goal and then start over again if you reach the goal.

Mike Bryant has a nice article on some of the characteristics of fixed frational position trading here:
http://www.adaptrade.com/Articles/article-ffps.htm

Later Ryan Jones came out with a revision to this type of money management strategy which he called Fixed Ratio Money Management - again Mike Bryant has a nice explanation:
http://www.adaptrade.com/Articles/article-frps.htm

As mentioned above these strategies (at least as I understand it) lend themselves to suggesting how many contracts/shares to hold given a certain strategy - something that falls into the variable portfolio.

While I haven't thought about it much rebalancing is a sort of money management strategy as well.

[blackomen]

Another idea to keep in mind is that leverage is normally an expression of maximum optimism in a certain approach to investing.

We know from history that periods of maximum optimism are often followed by periods of sub-par performance. 

If too many people start talking about using leverage with the PP, I would anticipate a period of PP returns that are below interest rates on margin debt.  That just seems to be how reality deals with such things.

Might considering studying the feasibility of a leveraged PP as a dissertation topic if I ever go back to school to pursue a PhD.. 

[stone]

I guess it all boils down to whether you mind loosing all your money and whether you want to get a lot more money. My aim is to preserve the value of what I have until I need it. If your aim is to have a pop shot at becoming rich then that is quite different. I'm struck by how some people who work as traders using wacky leverage strategies then put their own personal money in utterly basic low risk investments.

It's kind of fun to think that you can do a Phd in trading. Is it just about how the trading works for the trader or about how it influences the wider market etc?

Medium Tex, you saying about leveraged PPs being prophetic might also apply to people who simultaneously have a PP and a mortgage???

[stone]

Clive, that Personal Asset Trust also has stuck to those sort of stocks. It does look tempting as a plan B alternative to having everything based on the PP strategy.

I have segregated the stocks within our PP as three  investment trusts. CTY has the stocks of that type; BRSC has small volatile stocks and TEM is emerging market. Like you, I guess that for now it would be best to only have the consumer staple type stocks but I'm also convinced that I need to ignor my guesses . I did not realize at all that LTT would outperform gold this year etc etc.

1930 to 1950 spanned WWII, that is hopefully not what we are facing. Who knows, perhaps brands like Coco Cola will be passe in two years time but there will be a raging demand from Thialand or somewhere for some highly "cyclical" product -cars or something like that.