Alpha Generation and Risk Smoothing using Volatility of Volatility
Volatility of returns has been studied extensively in the literature but volatility of volatility (vovo for short) has been given very little consideration. This paper takes an expository look at vovo and discovers some remarkable results and concepts. These include alpha generation and risk smoothing strategies along with tactical asset allocation insights. Most of these results are quite novel due to the lack of current research on vovo.
The paper starts with a discussion of the mathematics of leverage. It produces a formula for the optimal leverage of an investment for a given market environment. It may come as a surprise to some that there is an optimal leverage since it may seem that if the return from an investment is greater than the cost of borrowing then the more leverage, the better the return. However, it is shown that volatility exerts a drag on the return of leveraged investments and the drag, being a squared function of return, eventually overwhelms any extra return that comes from using leverage.
Leveraged Exchange Traded Funds (ETFs) are used to illustrate the principles. We show how ETFs can be used to implement continuously dynamic leverage. We also clear up a myth about long term holding of leveraged ETFs. Sample data id shown from a number of stock markets including data from as far back as 1885.
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