## The Leveraged Leveraged Portfolio

February 12th, 2017

## The Leveraged Leveraged Portfolio

This is part of my post-test analysis of the last three articles I wrote (see list below). All the tests were ran on Quantopian servers using their data under the same conditions as everyone else. I used a slightly modified version of the program found on their site.

The original cloned program used (The SPY who loved WVF) showed a 22.43% portfolio CAGR over its 6-year test. And this, while using 3x leveraged ETFs. If you did the math to convert the thing to a no leverage scenario, the CAGR would drop. There were no leveraging fees in this ETF scenario since leveraging is included by design. But, this still made it a 3x leveraged portfolio.

To put it more in perspective. It would have required a \$30k initial capital (3x) to obtain the same output as the original. And this would have translated into a much lower CAGR. The calculation being: (34,291/30,000)^(1/6.09) – 1 = 2.22%. Not that great a solution considering.

But then again, you could borrow the added capital. To make it profitable requires a higher portfolio return than what will be charged on the loan.

The calculations for this is: A(t) = A(0) + n∙u∙PT – (2/3)∙A(t)∙((1+0.03)^6.09 -1), assuming a 3% interest charge. In the \$10k original scenario, at 3 times leverage one has to pay loan interests on 2/3 of the ongoing account value to benefit from the use of 3 times the initial capital. This gives the same profit as the 3 times leveraged ETF scenario. The charges for the \$10k scenario would be \$3,382 reducing the CAGR to 20.36%. This is better than increasing the initial capital. An approximation could have been done using: A(t) = A(0)∙(1 + 0.2243 – 0.03)t = \$29,486, which is close enough.

For the \$1 million scenario, the charges would have increased but so would have the outcome. The trading strategy was shown to be scalable (see table below). And, based on the equation above, charges would now amount to: \$338,094. But still generate a 20.35% CAGR, for a net profit of \$3,090,277 on the \$1 million initial stake.

 #1  Summary Report  Original Program (without modifications)

(click to enlarge)

 #2  Original Program - Portfolio Metrics

(click to enlarge)

With my modifications, leveraging 2 times, would require paying out interest charges too. My equation for this would be: A(t) = 2∙A(0) + 2∙3∙n∙u∙PT - ((1/2)∙A(t)∙(1+0.03)^6.09 - 1)

And since the initial stake was \$1 million, the charges alone for Test one would be: \$8,482,085 for the period. The strategy would be able to benefit and not pay for what the 3x leveraged ETFs brings to the party. Test one would still end with: \$78,938,527. A CAGR of 104.90%!

 #3  Summary Report  with (1+g)t and boosters (and CAGR corrections)

(click to enlarge)

Using leverage is a matter of choice and of potential benefits. It depends on a strategy's performance level. It the strategy does not outperform the leveraging charges, it becomes a losing proposition.

But, as long as the added performance in CAGR terms is above its costs, there is a profit to be had by leveraging.

Some trading strategies have a hard time supporting leverage. But, it should be noted that in this case, even with my modifications, the program supported leveraging for 2,222 days. And that is a stretch. It is sufficient to acknowledge that the underlying trading procedures have merit and deserve more investigation. At least, they have shown that not only they could survive over the past 6 years, but they also could thrive. And this even if there were added costs.

Could this break down going forward? Yes, sure, maybe. But, it is the responsibility of the strategy designer to program his/her trading strategy in a way to minimize foreseeable contingencies. Design protective measures for the just in case. You have advance notice that the market is uncertain, you can program now for what you would want your program to do going forward.

It is worth noting that during the 2,222-day test, one could have quit the game at any time and finish ahead.

 #4   Performance Chart - Test 3 with (1+g)t and boosters

(click to enlarge)

My modifications benefited from a 6 times leveraged portfolio at a cost of a 2 times scenario.

Follows the summary portfolio metrics as generated by Pyfolio (a Quantopian utility program made to analyze such things).

 #5   Portfolio Metrics  with (1+g)t and boosters

(click to enlarge)

This can open up another class of trading strategies: the leveraged leveraged portfolio. And based on the above metrics, they could really fly!

See related articles: