Sold the rest of those GLD puts

In a post earlier this month ("Buying a lottery ticket to bet against gold") I mentioned buying a few puts on the gold ETF GLD. Those puts I bought were the Jan 10s with a strike price of 108, GCZMD.X. I got them at $0.74. I sold half on 12/11 at $2.92 for a gain of about 390%. Today I sold the rest at $3.20, for a gain of about 430%. I'd send Buffetteer17 a nice bottle of scotch if I knew his address.

Buying a lottery ticket to bet against gold

I've mentioned the pseudonymous GuruFocus commenter Buffetteer17 before, noting that he is probably the savviest and most numerate of the commenters on that site. There's a lot more chaff than wheat on GuruFocus, but I usually read Buffetteer's posts with interest. He wrote this in a GuruFocus comment thread today:

According to the Sornette bubble detector formula, the gold price bubble is nearing a critical point, meaning there's likely to be a large correction in the next few weeks. I applied the formula to GLD price history going back to March and got several high quality fits, with an R-squared in the range of 92-94%. You can clearly see the faster-than-exponential price rise on a log price plot. The critical dates range from 11/27 to 12/4. I bought a few Dec 09 and Jan 10 put options on GLD as a lottery ticket.

At this point, a commenter mentioned the devaluation of the dollar as the cause of the spike in gold prices. Buffetteer's response:

Gold prices in dollars are going up super-exponentially, way too much to be explained by dollar devaluation. Maybe dollar weakness is an underlying cause, but the gold price is now disconnected from that. We're seeing herding behavior. The motivation seems to be buy gold because other people are buying it and the price is increasing.

As I noted in my own comment on that thread,

I had a related exchange with Aaron Edelheit, after he wrote a post saying people should get out of cash because of dollar weakness. My guess is that when we get the inevitable stock market correction, the dollar will rise as it did last time, and gold will drop. The longer term trends might be different, but that seems like the most likely near term scenario.

I piggybacked on Buffetteer17's idea here and picked up a handful of Jan 10 puts on GLD today.

The Half Kelly bet

One of the smartest and most numerate commenters on GuruFocus is the one who goes by the pseudonym "Buffetteer17". Here is Buffetteer17 recently expounding on the merits of a modified version of the Kelly formula for optimally sizing bets or investment positions:

The half Kelly bet has some interesting mathematical properties. For risk management purposes, the nice property is that it cuts your risk of temporary loss (i.e., volatility) by a large amount while reducing your return expectation only a little. The other important property of the half Kelly bet is that it gives a large margin of safety in the risk estimate. If you are off by a factor of two on your risk of loss estimate, a full Kelly bet will reduce your return expectation to zero. But a half Kelly bet will leave you with 2/3 of the return expectation. Not surprisingly, underbetting is far, far safer than overbetting.

With the full Kelly bet, your probability of temporary loss is a linear function of the amount of loss. For example, you stand a 90% chance of losing 10%, an 80% chance of losing 20%, a 50% chance of losing 50%, etc. Not many investors are comfortable with the prospect of a 50% probability of losing 50% of their money. With the half Kelly bet, your probability of temporary loss is a quadratic function of the amount of loss. For example, you stand a 81% chance of losing 10%, a 64% chance of losing 20%, a 25% chance of losing 50%, etc.

Your expected gain with the half Kelly bet is reduced by 25%. For example, if your expected gain is 40% with the full Kelly, it is 30% with the half Kelly, if your expected gain is 30% with the full Kelly, it is 22.5% with the half Kelly, and if your expected gain is 10% with the full Kelly, it is 7.5% with the half Kelly.

The quarter Kelly bet is even safer. You cut your volatility by a quartic factor while reducing your return expectation by half. For example, you stand only a 6.25% of losing half your money. If you can find enough uncorrelated bets to get all your money invested, you can still invest 100% of your stake with a high safety factor with multiple quarter Kelly bets. The rub, of course, is that it is hard to find truly uncorrelated bets during a market crash like 2008.

In his brief book The Dhando Investor, Buffett wannabe Mohnish Pabrai devoted a chapter to the Kelly formula before concluding that, rather than follow it exactly, he was motivated by it to aim for a 10x10 portfolio (ten positions each comprising 10% of his portfolio). According to notes on his annual investor meeting earlier this year, Pabrai has moved further away from the Kelly formula, to a 3-5-10 set up, where he will only allocate 3% or 5% to most positions, and only occasionally allocate 10% to one idea under extraordinary circumstances.

A problem I have with this gets to a key difference between investing in stocks and betting. Stocks have their own idiosyncratic risks and potential upsides, and the more of them you own, generally, the less informed you will be about them. Better to dig deep and bet big on a handful of stocks with high upside potential, in my opinion, than to broadly diversify as Pabrai is doing. Even broadly diversified index investors got their heads handed to them last year. Idiosyncratic risks aren't the only ones out there, and in over-diversifying to eliminate them, you also diversify away the idiosyncratic high potential returns associated with individual stocks.

Notes from an Investor Who Avoided Large Losses This Year, Part II

Below is the continuation of Buffetteer17's notes on his hedging strategy (click here for Part I):

A few words about those S&P 500 index put options. I bought them at market highs last year. I was concerned that The Portfolio was doing too well. In Oct. 2007, it was yielding a CAGR of 39%. And that was return on assets. The return on equity was higher, about 50%, since I was about 20% on margin. While I might dream that I was the second coming of young Warren Buffett, when I woke up, I knew it wasn't so. It was largely luck, leverage, and a 3 year bull market, and---perhaps---a little bit of skill. I did not predict the bottom would fall out of the market, but I did consider what would happen to a leveraged portfolio if it did. So I decided to sacrifice a few percentage points of returns in exchange for market crash insurance. I bought S&P 500 index puts with a face value (sum of strike prices) of about 2x the size of The Portfolio. Average strike price was around 1250 and average time to expiration around 18 months. The two key objectives were to put in a floor below which The Portfolio is very unlikely to fall, and to provide funds to meet margin calls if they come. Most of my put buying was around S&P 500 level of 1500-1550, so the options would not protect much against moderate drops, say 20%. But they would become extremely valuable on a drop of 40-50%. The cost of the puts was about 6% of The Portfolio. Given that the lifetime of the options is about 18 months, and that the cost is deductable (assuming they expire worthless), this would hurt my total return by about 3%/year. As it happened, the damage is already reduced to about 1%/year, since I sold a few the puts on 1/22/08 and 3/7/08 for incredible percentage gains. Without the puts, my loss this quarter would have been 22% instead of 16%. The puts don't really fully kick in until S&P 500 level of about 1250.

Q2-08 (hedge 13.2%) The hedge comprises a number of S&P 500 index put options, with a face value (sum of strike prices) of about 2x the stock portfolio, with strike prices varying from 1350 to 800, and expirations of 12-18 months. The hedge is doing its job fairly well. That job is to insure against margin calls and put a floor under my net worth. The floor turned out to be a little lower than I planned, because my stock portfolio declined faster than the S&P 500 index. During the market dip in late June, I sold down a little. This reduced my basis cost for the options to 2.5% of my portfolio and the remaining options are up 186%. I'm in no danger of being forced to sell undervalued stocks due to a margin call. If the S&P 500 drops further and my stocks drop proportionally, I'll actually gain quite a bit, since the options are now sufficiently close to the strike prices that they have quite high deltas. I estimate that the existence of the hedge has added 3.7% to my returns since inception.

Q3-08 (hedge 10.8%) The hedge comprises a number of S&P 500 index put options, with a face value (sum of strike prices) of about 1.5x the stock portfolio, with strike prices varying from 1250 to 800, and expirations of 12-18 months. I bought the hedge a little over a year ago, at a cost of about 4% of the portfolio value. I had no idea that the stock market would crash and the economy would enter recession. But I was concerned about the collapsing housing market and early hints of a credit freeze. I figured I would take out some cheap insurance, just in case. The hedge is doing its job fairly well. That job is to insure against margin calls and put a floor under my net worth. The floor turned out to be a little lower than I planned, because my stock portfolio declined faster than the S&P 500 index. This quarter I sold about 1/4 of the options. By now, the profit from the hedge is so much that even if the remaining options expire out of the money, the hedge has more than paid for itself. This has been by far my best investment of the year, with returns north of 300%/year. Too bad I didn't put more money into it.

Notes From an Investor Who Avoided Large Losses This Year, Part I

An individual investor who goes by the name "Buffetteer17" on GuruFocus avoided large losses this year by hedging his portfolio. Below are his notes explaining what he did on a quarterly basis. This is long, so I've broken it up into two posts.

History of the Hedge. Every quarter, I do a writeup on my portfolio, so I can recall what I was thinking and review previous mistakes. Here are excerpts from the quarterly reports, starting with the Q2-2007 one. Apologies for the repetition, but I wanted each quarterly writeup to stand alone.

Q2-07: (hedge 1.0%) I started a small hedge position, comprising S&P 500 index puts with various dates going out about a year, and various strike prices around 1200-1300. The purpose of the hedge is to make it safer for me to use debt and margin to buy stocks. The portfolio yield has stayed in a band from 20% to 30%/year, after tax, for a couple of years now. I can borrow money at an after-tax rate of under 6%. Why not borrow at 6%, earn at 25%, and pocket the difference? The answer of course is risk; a serious bear market could easily reverse that 25% to minus 25%. There is also the risk of a margin call, disrupting the portfolio by forcing me to sell great companies at depressed prices. But if there is a serious correction or bear market, those S&P index puts will become extremely valuable, giving me something besides good stocks to sell to meet margin requirements. It may sound like I'm going way out on a limb, but I'm not. I'm limiting my margin debt to about 20% of capital. The hedge, incidently, is actually currently making a profit, since I bought the puts at market peaks. However, my fervent hope is that hedge expires worthless. It is strictly insurance against severe market corrections.

Q3-07 (hedge 2.8%) I slightly increased my hedge position in S&P 500 index puts with strike prices around 1250, and I will keep it going as long as I'm using margin debt. Currently margin debt is around 30%. Oddly, I've actually made a small profit on the hedge, since the S&P 500 has gone down a little since I started it. With the present combinination of high returns (32%) and high margin debt (30%), I feel quite comfortable paying the 2%/year or so that the hedge is likely to cost me for insurance. At some point, I will pay off the debt, and rethink whether the hedge is a good idea.

Q4-07 (hedge 6.8%) The Portfolio is fairly highly leveraged right now, at about 35% margin loan. This leverage was mostly taken after the big Nov. drop in the market, to pick up bargains. Hopefully, the 6.8% of S&P 500 index puts will give sufficient protection against margin calls if the market tanks in 2008.

Q1-08 (hedge 13.1%) I entered the quarter more than fully invested, about 130%, and ended it about 150% invested. I wasn't very active...Actually my S&P 500 index put options were up more than anything else on a percentage basis this quarter, 48%, but I consider them insurance rather than a for-profit investment.

Click here for Part II