Geoff Considine

Stress Testing Your Portfolio

Correction:

Ron is correct: Bob's portfolio would have lost 19% of its value even without any withdrawals. Before withdrawals, the stress test formula proposed in this article would suggest a 'worst case' of 8.7% - 3*10.6% = -23%. Had Bob done the stress test ahead of time, he could have tuned down his risk level if this was too severe blow. Bob did not have a very well diversified portfolio (according to QPP) and I am in no way saying that this was a great portfolio choice. My point is that a Monte Carlo model, properly stress tested, would have alerted Bob to the risks in his portfolio.

I emphasize: Milevsky's point (and I agree) is that we can never be sure whether we estimate the probability of extreme events well--but we can stress test to see if the 'worst case' events that we can estimate are survivable.

On a related note: there have been some famous cases in which quant models have predicted that the things that hit their portfolios were 25 standard deviation kinds of events--i.e. effectively impossible. This was true in 08 and also in the case of LTCM. The models were clearly wrong. 3 standard deviation events do happen, and we are also saying that we know that they will probably happen with greater frequency in real life--which is why stress testing to ensure survivability of such events is so important.

Opportunities in Options Markets, Summer 2009

John:

Thanks for the comments. Obviously one can sell puts vs. selling covered calls--one is just the synthetic of the other. The issue comes down to how confident you are in future volatility--the cost of rolling the strategy forward through time.

I agree that Bodie's strategy is far more conservative than what I am proposing.

I have been focusing on selling long-dated options--like what I use in my examples.

Geoff



On Jul 02 02:46 AM ikkyu wrote:

> Greetings Geoff,
>
> Nice to see the evolution of your thoughts about monte-carlo and
> options pricing. I think this is the most interesting stuff you have
> done to date.
>
> Please let me ask a few questions, if you don't mind.
>
> Not sure why underpriced options would suggest buying calls rather
> than buying puts (or more reasonably straddles) in the short run
> (<3 years). Serial correlation can be positive with a negative price
> trend, can it not?
>
> Also, are you talking about buying OTM calls on EBAY? While stock
> markets tend to go produce positive results over long periods, you
> have to have to inherently predict the magnitude of the move when
> buying options.
>
> Which options are you talking about selling? The long dated LEAPs
> or the front month? You would have interest rate risk on the LEAP,
> far lower gamma initially, and wider bid-ask spreads. I usually divide
> the time value by the number of days till expiry to get a better
> idea of the decay per day.
>
> Also, why sell covered calls at all? Naked puts would be the risk
> equivalent and would simplify things. If you get exercised, you could
> then start selling calls on the underlying.
>
> While i like your plan, it is clearly not an equivalent for Bodie's
> conservative methods. Bodie's plan seems like it would work better
> with a call spreads. It would be like your own index annuity. <br/>
>
> Just some thought. Nice piece of work. Seems like you are definitely
> thinking out of the box.
>
> Cheers from Osaka,
> john
>

Opportunities in Options Markets, Summer 2009

This is just using QPP's projected volatilities for each ticker and the rest of the tabel is other data. Or did I miss your question?


On Jul 02 02:54 PM gasem wrote:

> How do you use QPP to generate the above table?
>
> thanks

Stress Testing Your Portfolio

Actually, my 3SD loss is worse than what happened over the last two years by notable amount. You are missing the subtlety of Milevsky's proposal. We can never know the tru probability of really extreme events all that well--even if the world is Gaussian, we would have estimation error on the mean and SD. Milevsky's is suggesting taking a model's estimate of 'worst case' and making sure that it is survivable--this is very reasonable. You are saying that the test is 'historical maximum drawdowns' which is also reasonable, but will tend to mack really high loss potential. Many firms have not existed long enough to truly test the extremes in real life--thats why we use models in the first place.


On Jun 19 07:23 AM MachineGhost wrote:

> > but I am hoping that the 3SD worst estimate is still a good

Stress Testing Your Portfolio

BlueOkie:

Nothing in QPP or Monte Carlo is inherently backward looking, though plenty of Monte Carlo implementations are just that way. QPP has been tested extensively as a forward looking tool--and its results speak for themselves. Also, nobody rationally suggests that investors will never change pathes--I wrote an article showing how this relates to Monte Carlo and how a combination of MC and the flexibility to adjust your plans dramatically increases your odds of success. BTW, who said anything about living to be 120?

Geoff


On Jun 17 08:59 AM BlueOkie wrote:

> Monte Carlo is an excellent tool. The problem is what you input for
> the variables. Bob is a person and will alter his behavior given
> a changing environment. Monte Carlo works in hindsight and in a class
> room. The probability of event "A" in 2006 may not be equal of "A"
> 's probability in 2007 or even any of the future years. Finally,
> why would you look at the probability of Bob living to 120?

Stress Testing Your Portfolio

I am not accounting for the increase in autocorrelation / cross correlation that occurs in a major meltdown but I am hoping that the 3SD worst estimate is still a good measure. Basically, we are saying that we plan for a really bad (<1/1000) event while ignoring autocorrelation/correl... increases and this is used as a reasonable estimate of the worst case that investors must plan for, given that we know that this will under-estimate the probability of such an event. In light of 2008-2009, this look very reasonable. My estimated worst case 1-year using this simplified approach was worse than 2009-2009 for all the portfolios I have examined.


On Jun 16 05:18 PM gasem wrote:

> In terms of stress testing how do you view changes in a portfolios
> diversification metric and auto-correlation metric
>
> As I watch things evolve I saw diversity nose dive and auto correlation
> explode

Stress Testing Your Portfolio

Guys:

Thanks for all the comments. I am running a bunch more cases right now using this stress test metric. I am looking now at the two year period ending in May 09. This fills out the picture. I will post my next article with more of these results.

Cheers,

Geoff

Stress Testing Your Portfolio

On Jun 12 01:09 PM Analyste de Boston wrote:

>In truth, there were many, many more
> +65yo Buy&amp;Holders with >70% allocation to eqty in 2007.

Yes, but that is precisely the kind of over-aggressive stature that Monte Carlo tools like QPP help to warn against.

Stress Testing Your Portfolio

Hi guys:

I enjoyed the comment stream today, after being away for the weekend. What I find most striking is that this topic has not gotten more attention in the media. There was the really poor WSJ article on Monte Carlo, but you guys are really hashing out the important issues. I agree with the comment on market discipline--the hardest thing for people to do is to stay with a plan--if they have a plan. I am sure that there are lot's of Bob's in the world who sold their equities and purchased an annuity just before the market rallied 35% or so in early 2009. I think that Monte Carlo tools can help investors to be more cognizant of thr risks and thus choose a level of risk that they can live with. Back when QPP was projecting a doubling in volatility over recent years (in 2007), I saw very little commentary on this issue. THAT was the time to prepare. After the crash, there are many people who have been crushed and I am well aware that what Gasem says is true: there were many people aged 60+ with very high allocations to equities--and largely undiversified exposure to equities, too. Monte Carlo is not a crystal ball, but it can provide guidance that helps investors avoid taking too much risk. Also, I am totally sympathetic to the ideas that there are much better portfolios than Bob's--I agree. The specific portfolio is simply a straw man.

Also, Analyst de Boston says that his market timing made his investors 61% in this bear market. First off, I tip my hat :) Second, Monte Carlo does not mean that you do not use tactical asset allocation methods--I have written about this. In the case shown here there is no Tactical component, but this is just one case...

Geoff

The Road Ahead for Investors

Guys:

Thanks for all of the thoughtful comments. The spread of thinking that you all have expressed mirrors what everyone feels--the balance between long-term statistics and the current view based on the specifics of the situation. I am not an raging bull--that should be clear. When I look around, there are clearly some serious issues and we don't know where things will go from here in the near term. If the government persists in propping up bad banks, we could see a situation like Japan--with a sort of 'walking dead' market for quite a few years. We are in a remarkable situation--think about oil--going from $145 to about a third of that in just a few months. The degree of deleveraging is amazing. A great deal of how one responds to this market will depend on the rest of one's portfolio (human capital, household debt, etc.). If we see a prolonged period of deflation, debt will overcome many more investors. When the market reverts to double digit inflation for some period (as I fear it will), we will see investors with high allocations to FI lose purchasing power. I have no problem with the notion of timing, but it is very dangerous to ignore the possibility that your timing may be wrong. In the same way that so many people went high Beta and disounted risk before 2008 (ignoring all other risks), there is a peril in having too much faith in your own singular view--whether its the potential of emerging markets or to discount inflation or to shun market risk.

Anyway--thanks for this dialog.

Geoff

Opportunities in a High Correlation World

PiedPiper and JLBR:

I agree with both of you. Correlations temporarily spike up when people start to think the world is ending. This both makes SAA less effective and makes tactical strategies more effective--but both of thes effects are not long-term. When people are indiscriminately fearful or optimistic, there are opportunities and we are in the former. With regard to small caps--this is something I have been thinking about, too. In the past, blue chip stocks were large cap and also perceived as safer. We have learned an important lesson in this regards. Certain large cap stocks have been exploding spectacularly--market cap is not a signal of "quality".

Opportunities in a High Correlation World

Eric:

See the following discussion:

www.prweb.com/releases...

The original research paper describing the analysis is here:

www.quantext.com/Econo...

Geoff

Income Planning and Safe Withdrawal Rates

Gina: QPP allows you to test the idea you are referring to with a single setting--and of course it works in terms of increasing the % draw and the survival rate, but the income volatility can be very high--so I also allow the user to specify a minimum required draw (i.e. what you need to keep the lights on.).

Geoff

Defining a Set of Core Asset Classes

I will try to cover a range of questions here. With regard to bonds vs. bond funds, this depends very much on your personal situation. In a hypothetical world, bond funds and bonds accomplish the same thing in a portfolio.

With regards to infractructure, if you look at my All ETF model portfolio, you will see that I have utilities, transport, and materials as specific allocations--these are all infrastructure. These come up simply because they have such nice portfolio effects via QPP. I am awaiting a copy of Mr. El-Erian's book to see how he motivates these asset classes in depth.

With regard to the recent losses in commodities: the whole point of asset allocation is offsetting risks. Commodities have had a great run but they cannot out-perform forever. Also, risk and return go hand in hand--you cannot have the returns of commodities unless you take on the volatility. This brings us to the broader issue of whether timing makes sense, etc. I have written about this elsewhere: of course relative value is important--but history suggests that it is secondary to some other factors.

Geoff

Defining a Set of Core Asset Classes

Ranger Ric:

Thanks for your comments. The fact that small cap and large cap are highly correlted does not alter the fact that small caps, with higher risk, also yield higher average returns--this is in no way contradictory. A small cap tilt will result in higher returns--no mystery. Equal weighting a portfolio creates such a small cap tilt.

Your point about the stability of correlations is correct, but I have found in long backtests that the stability of the correlations is sufficient via QPP to yield good portfolio outlooks--I have tests going back thirty years in three-year out-of-sample increments. Also, to be clear, QPP does not strictly preserve linear correlations.