Leveraged Funds, Beta, and Berkshire

BACKGROUND

As we know index funds like SPY are popular among passive investors however there exists a breed of leveraged index funds like SDS and SSO that help investors achieve higher levels of risk which may bring higher reward. We will assume a risk-free rate of 0.1% per month.

SSO is a 2x leveraged S&P fund, in a given day it will double the performance of what SPY does. You will get returns almost as if you have double the amount of money in SPY. For the period of July 2014 to June 2019 SSO has an average monthly return of 1.67% with a standard deviation of 7.06%.

SDS on the other hand is an inverse 2x leveraged S&P fund, in a given day it will mimic SPY by two times in the opposite direction of its performance. Funds of this kind are convenient if you want to bet against an index but don’t want to have to short sell shares either because of an inability or personal preference. For the period of July 2014 to June 2019 SDS has an average monthly return of 9.94% with a standard deviation of 70.92%. It should be noted these return numbers have been skewed by this particular data range.

BETA & PORTFOLIO MANAGEMENT

Using SPY as the market portfolio the calculations of beta come out to:

SSO: 1.9503

SDS: -3.744

What we care more about than just these individual beta numbers is what portfolio allocation will provide us with a moderately aggressive portfolio beta of 1.5? A portfolio with 92.09% SSO and 7.91% SDS will create a portfolio with a beta figure of 1.5.

In the scenario that you target a monthly return of 1% you will have a portfolio allocation of 108.1% SSO and -8.1% SDS. This allocation would result in a beta of 2.4116 which is beginning to get into the high risk levels of beta.

RISK & RETURN

Standard deviation of a securities monthly returns is an easy way to get a first glance on the level of risk the holding may carry. However, beta is a more useful measure of risk level because it's in proportion to the market itself; in this case SPY. This is relevant to the construction of your portfolio because it highlights what holdings may not be a good idea to invest in. For example, if you owned 100% SSO, you’d bring in about 1.67% a month while being exposed to a beta of 1.95. If you now add in SDS to diversify and target a lower monthly income of 1%. Your allocation will make it so that you have a beta of 2.4. This is the exact opposite result of the expectation from diversifying.

ABNORMAL RETURN AND ROLLING REGRESSION

Beating the market is an often misused term as truly beating the market is generating positive alpha as opposed to just getting higher return than the S&P. Let’s take Warren Buffett’s BRK-A for example it has an overall beta of 0.837658 meaning it is slightly less risky than SPY so does it generate positive alpha?

To see if BRK-A has generated positive alpha we will look at yearly averages of monthly alpha based on the beta from the 5 years prior to the one in question.

From 2014-2016 Warren Buffett and BRK-A only generated positive alpha two out of the three years we have looked at. The average of all three years is 0.23% which means the abnormal return they have achieved is not too far above the Capital Allocation Line. This makes sense in respects to Warren Buffett, he is known for being patient and passively investing as opposed to generating high amounts of positive alpha like a hedge fund.