Investing in Leveraged Index Funds

Abstract

Standard financial models predict that investors who are willing to hold an investment in the short‐run will hold the same investment for the long‐run. It is well known that a leveraged investment's expected excess return is equal to the unlevered excess return scaled by the leverage factor. Volatility is likewise scaled‐up by the leverage factor. It is not so well known, however, that the realized terminal wealth generated by the leveraged investment is very likely to be significantly lower than its expected value. This is true because leverage induces positive skewness into the distribution of long‐run wealth. The skewness and hence the probability of achieving a lower‐than‐expected terminal wealth increases with the length of time that a leveraged investment is held. Even for moderate leverage factors, this effect can be so dramatic that the leveraged investor will lag behind the unleveraged investor.