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Leverage without leverage

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Diversification vs leverage

Some of the most famous investors (Warren Buffett, Peter Lynch) are known for their disdain of diversification.

Bill Ackman has been expressing similar views recently too. Ackman is a self-professed devotee of Buffett so you might think he slightly misunderstood what Buffett meant. However, he is also known for his highly concentrated positions in stocks, so there was no misunderstanding.

As a hedge fund manager, he is also inclined to use leverage with his trades.

Options are a useful way to employ leverage, as if your view turns out to be wrong, the maximum loss is known upfront.

However, not every investor is in a position to use leverage at all. For example, a tax exempt IRA might well be restricted from trading options or selling stocks short.

So how can we employ leverage if we're not allowed to use leverage?

The answer is not to diversify too much.

More specifically, we need to buy high beta stocks.

The beta of a stock to a given market variable such as SPY or ACWI is the coefficient of a linear regression of returns of the stock against returns of the market (without an intercept). For an ordinary regression, this can be computed as the correlation of the returns multiplied by the ratio of the standard deviation of returns.

A stock will have high beta if it is more volatile than the market, and is also highly correlated to the market.

Source: Yahoo

Note that high volatility alone is not sufficient to be high beta.

There are stocks such as HUM which are significantly more volatile than the market, but have zero correlation to it, so their beta is zero.

If we have an equally weighted portfolio of 10 stocks, then the beta of our portfolio will be the average of the individual betas.

This sounds innocuous, but this fact explains precisely what happens when we diversify a portfolio.

The stocks in the portfolio are not perfectly correlated to each other, so the volatility of the portfolio is lower than the average volatility of the stocks that it contains.

Therefore, in order for the beta of the portfolio to be the average beta, the portfolio must necessarily be more correlated to the market than its components.

Source: David Woo Unbound

For example, in the picture shown, we formed a portfolio of all stocks in our universe for which the most recent beta is measured to be above 2.

On average the correlation of these stocks to the market is about 60%, but as a portfolio, the correlation is around 90%.

If we include more stocks, then the correlation to the market will necessarily increase.

Source: David Woo Unbound

For example, if we broaden our portfolio to include all stocks with beta greater than 1, then our portfolio will be over 95% correlated to the market.

Hopefully these observations are giving you some ideas.

For example, have you ever noticed that if you read about a particular index tracking fund, it always something to the effect that the fund will have at least 80% of its assets invested or some such.

The way that an index fund is likely to be run is to own all of the largest stocks in the index, but to skip some of the smaller stocks that have low beta and generally assign a little more weight to higher beta stocks. In this way they can get near perfect index matching while still maintaining a small cash balance, which is always useful.

One strategy that comes to mind is to try to replicate the market as well as possible using stocks with an average beta of 2. This would only require 50% of assets leaving us 50% in cash. The interest earned on this cash is compensation for the risk we are taking that our portfolio doesn't match the market as well as expected. If rates are high so that this interest is significant, we could use it to purchase some put options to give us some cushion if our picks are poor. This strategy is one reason why high interest rates might be viewed as a more favourable environment for stock pickers.

Another strategy that can be used in taxable accounts is to match the index with a relatively large percentage of the stocks, and to harvest tax losses on a systematic basis. When one set of stocks is sold to realize a loss, they can be replaced with similar alternatives that were not held. With this strategy, the tax benefit is our compensation for the risk that we fail to match the index with our holdings.

There's no free lunch here, but holding a portfolio of higher beta stocks provides some flexibility in our strategy for how to outperform the market.

For our macro regime switching portfolio, the idea is that we can outperform the market in up weeks through holding high beta stocks, and then we try to outperform in down weeks by getting out of the market. Our success will depend on both whether we can identify the high beta stocks that do particularly well, and whether we can accurately predict the best times to be out of the market.


I put in the VRX video just because that particular trade was one where the investment bank offloaded the risk to the hedge fund where I worked at the time. I recall a discussion about whether positioning in the stock was crowded, to which the answer was Ackman is a one person crowd.

VRX later changed their name to Bausch Health Companies because of the bad publicity around their pricing strategy. Our new holding AXON changed their name from TASER as well, perhaps because they thought that was bad branding too. I wonder whether companies which change their name generally do well or poorly?

HUM might look like it has negative correlation to ACWI, but in return space the correlation is approximately zero.

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