Long-Short Portfolio Optimization

Includes: SHY
by: Maurice Chia

In my previous article, I showed that there was only a marginal improvement in volatility for a given return between an optimal portfolio derived from a universe of 117 stocks and one derived from a universe with 187 securities.

Is there anything else we can do to improve efficiency?

Let's look at the following 11 stocks:

Bank of New York Mellon Corp (BK), Coca Cola Co (KO), ConocoPhillips (COP), Costco Wholesale Corp (COST), Intel Corp (INTC), Mastercard (MA), Moody's Corp (MCO), USG Corp (USG), United Parcel Service (UPS), Wal-Mart Stores (WMT), Washington Post Co (WPO)

Then add in the iShares Barclays 1 to 3 Year Treasury Bond ETF (SHY) as our risk-free asset proxy. Push these 12 securities into an optimizer and you get the following efficiency frontier. In this graph, the x-axis represents volatility (standard deviation) while the y-axis represents the average of daily moving annualized returns.

The yellow dot denotes an equal-weighted portfolio while the green dot denotes the optimized portfolio with similar volatility to the equal-weighted portfolio.

The optimal portfolio weights are as follows:

iShares Barclays 1 to 3 Year Treasury Bond ETF 40.2%, ConocoPhillips 13.6%, Costco Wholesale Corp 17.1%, Mastercard 21.9%, Moody's Corp 2.1%, USG Corp 5.1%

Long-Short Optimization

A long-short optimal portfolio is one where long buys and short sales are optimized as one optimal portfolio. This is distinctly different from combining 2 portfolios, long and short, which have been optimized separately.

The following is an example of an efficient frontier that is based on a structure with a net long position where individual long positions have a maximum of 80% and short positions have a maximum of 20%. It is not a long plus short portfolio. It is a long-short portfolio in the true sense of the word.

The long and short allocations for a long-short optimized portfolio with approximately the same volatility as a long-only equally weighted optimal portfolio are as follows:


Bank of New York Mellon Corp -20%, Intel Corp -20%, Washington Post Co -20%, United Parcel Service -20%, Wal-Mart Stores -18.6%


Moody's Corp 0.9%, ConocoPhillips 9.6%, USG Corp 12.8%, Mastercard 23.5%, Costco Wholesale Corp 42%, Coca Cola Co 29.8%, iShares Barclays 1 to 3 Year Treasury Bond ETF 80%

Summing the negative and positive allocations will equal 100% of your integrated Long-Short portfolio. The next step would be to find the individual allocations for the long and short portions (dropping the minus signs) so the totals equal 100% for each portion:


Bank of New York Mellon Corp 20.28%, Intel Corp 20.28%, Washington Post Co 20.28%, United Parcel Service 20.28%, Wal-Mart Stores 18.86%



Moody's Corp 0.45%, ConocoPhillips 4.83%, USG Corp 6.45%, Mastercard 11.83%, Costco Wholesale Corp 21.15%, Coca Cola Co 15.01%, iShares Barclays 1 to 3 Year Treasury Bond ETF 40.28%


In dollar terms

If you have $100,000 to invest, this translates to a $33,176 allocation for your short portfolio and $66,824 for your long portfolio inclusive of $26,918 in your risk free asset.


Bank of New York Mellon Corp $6,729, Intel Corp $6,729, Washington Post Co $6,729, United Parcel Service $6,729, Wal-Mart Stores $6,258

Total Short: $33,176


Moody's Corp $303, ConocoPhillips $3,230, USG Corp $4,307, Mastercard $7,907, Costco Wholesale Corp $14,132, Coca Cola Co $10,027, iShares Barclays 1 to 3 Year Treasury Bond ETF $26,918

Total Long: $66,824


Using a Long-Short Optimized portfolio can improve the expected return of your portfolio for a given volatility. But using short sales has its own set of risks outside of volatility. While investing long limits your total possible loss to the amount you have invested, the amount you can lose on a short sale (i.e. when the stock goes up instead of down) has no theoretical limit. Here are two articles for further consumption. The first one tells you how much extra risk you take with short sales and the other article, while being a little bit technical, is an excellent explanation on the possibilities of an integrated approach to a long-short strategy.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.