Volatility Pumping Through Rebalancing and Kelly Growth

# Volatility pumping in practice


# Volatility pumping in practice












The fascinating thing about volatility pumping (or optimal growth portfolio, see e.g. here) is that here volatility is not the same as risk, rather it represents opportunity. Additionally it is a generic mechanical strategy that is independent of asset classes.

My question: Do you know examples where volatility pumping is actually implemented? What are the results? What are the pitfalls?

## Answer by olaker (score 13, accepted)

https://quant.stackexchange.com/a/354

The optimal growth portfolio is obtained by applying the Kelly criterion which is one of the pillars of the sound risk management.

Ed Thorp's weekend forays to Las Vegas to play blackjack were one of the first historically documented cases of successful practical implementation of the Kelly strategy. Since then this method and its modifications have been systematically used by Thorp himself and other hedge fund managers as an important risk control tool.

## Answer by vonjd (score 6)

https://quant.stackexchange.com/a/7487

Here is an interesting example which makes use of these concepts in emerging markets. Emerging markets are ideal because volatility tends to be higher so it can better be harvested:

Diversifying and rebalancing emerging market countries by David Stein et al.

Abstract:

> We discuss the diversification and rebalancing of Emerging Market countries. Emerging country risks are high and relatively uncorrelated, and the cap-weighted index is oncentrated. In the absence of prior information on returns, these characteristics lead us to expect that a structured rebalanced portfolio will out-perform a capweighted one over the long term. We study this phenomenon with a theoretical model of portfolio returns – this allows us to quantify performance advantages and understand what drives them. It turns out that, even though Emerging Markets suffer high transaction costs and unreliable information, pragmatic portfolio implementations with relatively little trading are still possible. For real implementation, we want to gain some confidence that performance benefits will continue into the future, so we review how the key drivers of excess performance have been evolving during the recent past of increasing globalization.

## Answer by pat (score 6)

https://quant.stackexchange.com/a/7493

It was discussed long ago by Claude Shannon and discussed a bit in Fortune's Formula.

> In the 1960s, Shannon gave a lecture in a hall packed with students and teachers alike in MIT, on the topic of maximizing the growth rate of wealth. He detailed a method on how you can grow your portfolio by rebalancing your fund between a stock and cash, while this stock stays in a random ranging market. (He used a geometric Wiener example). Essentially, you buy more when stock price is low, using the cash at hand, or sell more when stock price is high, with allocation of 50-50% value at each interval.

In addition, the ideas were further explored by Thomas Cover, with his Universal Portfolios concept. There was some word that he had left academia at one point to work on a hedge fund.

Having done some research in this area myself, I can say that one of the issues is that it takes a very long time for the results to converge (i.e. it would take a great amount of patience for your portfolio to converge towards the best asset's performance).

## Answer by vonjd (score 4)

https://quant.stackexchange.com/a/63103

In the following blog post the analytical results of the following paper and reproduced by simulation with real market data:

Michael Stutzer: The Paradox of Diversification

> Abstract The current market malaise may keep some investors on the sidelines. The benefits of diversification may not seem as appealing in situations where the constituent investments are likely to lose money. Yet we will see, using relatively simple math, that diversification maintained by rebalancing can easily turn individual assets’ negative cumulative returns into positive portfolio cumulative returns. This seemingly paradoxical result is the investing analog of a well-known phenomenon studied by physicists and mathematicians, called Parrondo’s Paradox.

Parrondo’s Paradox in Finance: Combine two Losing Investments into a Winner

This is nothing else but the so-called rebalancing premium or volatility pumping.

In the blog post, some intuition is given and full R-code to reproduce the results. The results are derived by simulation of sample paths of binomial trees.

## Answer by Eduardo (score 1)

https://quant.stackexchange.com/a/7453

Here you have a example "applying Volatility Pumping to real stock market".

http://parrondoparadox.blogspot.com.es/2011/02/parrondos-paradox-stock-market.html