Volitility and Leverage

N

Norm

volatility (such as that measured by alpha or beta) and leverage (such as due to margin) are two distinct things. However, they seem to have some commonality with regard as to how they impact potential profitability and risk. It is generally possible to make or lose more money on high beta stocks than on low beta stocks. Similarly, it is possible to make or lose more money with leverage than without it.

Is there some way to equate volatility and leverage? That is, can you somehow say that trading a one instrument with a given high beta and not using leverage is equivalent to trading another
instrument with a low beta, but high leverage?

Better yet, is there a well defined mathematical relationship between volatility and leverage?

The reason that I ask is that I present trade high beta equities without using margin. I was wondering if trading a low volatility commodity, such as gold, with high margin (as is common with futures contracts), is in some sense equivalent with respect to potential for profit and loss to trading a high beta stock. That is, does the leverage of the gold contracts make up for the loss of volatility of the stock?

Norm
 
it's a good topic, i prefer the way you're doing it as well. if you can trade a higher volatility instrument with less capital and less leverage all other things equal, i think it's a better strategy

tons of leverage on a 'seemingly' low volatility instrument feels like a lot more risk. leveraging non-existant moves heightens the chance of blowing out capital vs the chance of just chopping around for a while with a small position on a more volatile asset and the chosen blend also has implications for granularity and transaction cost
 
Quote from Norm:

Better yet, is there a well defined mathematical relationship between volatility and leverage?
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Norm, I think you're talking about risk. There are some formulas out there to calculate risk based on beta (a measure of volatility) or VaR (it adds a prediction component to the risk calc, but the prediction is based on historical data. No magic). For example:

Stock X: 1000 shares, price $10, beta 1 = 1000*10*1 = $10,000
Stock Y: 250 shares, price $20, beta 2 = 250*20*2 = $10,000

The resulting $10,000 is your implied position, or dollar exposure. In facts these formulas hold true only for very diversified portfolios where the stock specific risk is less relevant (beta only measures the move of a stock relative to the market), and besides there are a few "little" problems that Beta or VaR formulas don't include. As Avid Consumer pointed out: liquidity, spread, commissions. I would add 'holding period' to the list.

IMO all these math formula are good for people who manage large diversified portfolios, or people who don't trade their own money, or people who trade on a simulator during their PhD. For day traders working on few positions at the same time these are approximations at best. Check out http://www.riskglossary.com
 
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