# Portfolio performance. Holding period return

What we would like to do now is to take our solver portfolio optimization model for a dry run and see how different allocation strategies are put together and evaluated for performance post allocation. We will introduce and use the concept of holding period return over two different observation periods. We will look at four different portfolio allocation strategies and will label them strategy A, strategy B, strategy C and strategy D.

To evaluate the results and compare the four strategies we need the ability to calculate holding period returns for the securities in our universe. We would like to measure holding period return across two observation periods. The first is the historical period of our dataset which we use for portfolio construction– which in our case is 8 years ending on 30^{th} June 2016. The second is our performance horizon – from the point of allocation – which is 1^{st} July 2016 to the point of review which is 31^{st} October 2016.

To calculate holding period return over a period pick two dates. A start date and an end date. Pick closing rates for both dates for all the securities in the securities universe. Then apply the return formula we have used so far in our calculation – Natural Log or ln(End date price / Start date price) for all securities. The resulting series gives you holding period return over the observation period.

For equities security prices can generally assumed to be dividend adjusted. But you should double check with your data source if this is the case. For bonds and currencies we can add coupon and deposit rate as a source of additional income over the holding period. For commodities if we are trading non deliverable or cash settled future contracts, there is no cost of carry. If we are trading and holding physical commodities a cost of carry has to be deducted.

There are two key points that we would like to make. When we allocate portfolios and compare results of one strategy with another, our portfolio metrics figure are calculated looking back in time. For instance when we compare the results of Strategy A with B and C, we see a big difference between A and B, but not that great a difference between B and C. We want to emphasize that this assessment is based on historical performance and there is no guarantee that we will see the same performance figures in the future.

It is only when we let the portfolio run with market conditions does the robustness of our allocation comes to fore. Till then our best case assumption is that the future will be just like the past. If that assumption holds our portfolio will do well, but if it doesn’t our performance will be disappointing.

For portfolio construction purposes have only used the data till 30^{th} June 2016 for a specific reason. We want our allocation to be independent of the most recent four months of market performance. The idea is to use market performance in the July – October period as a forward looking evaluation dataset for our different strategies.

While Strategy B and Strategy C may seem very close when we look at the historical data set, it is their performance in the forward looking data set that we want to use as a scoring and grading mechanism.

For the purpose of our initial analysis we will ignore bond coupons and dividends but we will come back and revisit the topic of incorporating dividends and coupons in our return calculations in a later note.

The three strategies we would like to examine are

- Maximize return per unit of risk with no short sales – S
**trategy A** - Maximize return per unit of risk with short sales allowed –
**Strategy B** - Maximize return per unit of risk with short sales and with portfolio alpha > portfolio beta –
**Strategy C** - A look back C where we look back on 31
^{st}October 2016 and pick securities that would maximize holding period return over the 4 month look back period to 1^{st}July 2016 –**Strategy D**

Our solver model for Strategy C and D forces Alpha excess return to be significantly higher than Beta and at the same time requires a minimum projected Beta return of 4%.

All four options limit allocation in a single position to less than 9%. There is also a limit assigned to maximum volatility – 9% but the actual optimal portfolio volatility can be lower.

When we run Solver with the three options here is what allocation and initial results look like at the point of allocation

Strategy A

Strategy B

Strategy C

B and C are quite similar except for our little hack with Alpha.

Now let’s run the three on the forward looking July – October data set

You can clearly see that there is a difference if we look at the holding period return over the 8 year period.

That difference becomes even more clear when we switch to evaluating holding period return over a our 4 month observation period.

Despite the fact that the original portfolio metrics limited to risk and return didn’t lead to significant differentiation between B and C (other than the Alpha hack), over the 4 month period, C had clearly out performed B. And the numbers are more impressive when we annualized them.

However before we congratulate ourselves note that the annualized return for both strategies is significantly lower than the expected average annual return calculated using the 8 year dataset. We know why that is? Do we?

If we restrict our allocation data set to the last two years, the suggested allocation by Solver will change dramatically. Using an 8 year allocation windows average out performances for both Apple computers and Yahoo and doesn’t completely highlight the impact of the recent downtrend in their prices. It’s not just Apple and Yahoo, within commodities markets also there has been a price route of sorts beginning November 2014. Currencies have also been in turmoil with both the Yen and the Euro heading in very different directions post the events of Brexit and the rate hike expectations in US treasury markets for the last two years.

Restricting the horizon to just the last two years allows us to allocate a significantly better portfolio. We can actually do better by taking our model one step further. Rather than allocating using our eight year backward looking set, we can allocate using our forward looking data set to find out the best of all possible allocations, given the recent four month performance of securities in our security universe. We will call this allocation Portfolio D. Our portfolio allocation with the benefit of look back over the last 4 months.

When compared with Strategy C, D tracks it except for a few key differences. The shorts are deeper when it comes to oil and the long position is more substantial in Gold.

What generated this performance? What was the contribution of each component of the strategy to the total portfolio return? This is a key question that we must answer when we dissect the performance of each one of our strategy. We take a look at strategy D and as a class assignment, please repeat the analysis for the other three portfolio strategies.

*From the EMBA Portfolio Management and Optimization course run at SP Jain’s Dubai campus from November 5th – November 10th. Also see the Portfolio management course resource page.*