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I've been reading up on different models used to forecast the equity risk premium, and I've seen a couple of papers that had questionable methods. For example, this paper by Javier Estrada goes into detail on how to use the Shiller PE ratio to forecast 10-year equity returns.

And this paper, which looks to be a draft, also uses a similar methodology to Estrada. The only paper I have seen where they specifically address the issue of independent observations and model misspecification is the one by Klement on using the Shiller PE in emerging markets.

The problem I have with the first two papers is that they look at the data available today and make a prediction about the next ten years. They then roll everything forward one month and make another prediction about the next ten years. Clearly, there are overlapping data between the two time periods. Should the authors only be evaluating model usability by looking at non-overlapping time periods? What is the most appropriate way to evaluate their models?

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3 Answers 3

Couple points I like to make:

  • There exists no reliable model that can even predict future price returns (risk premiums, excess returns, whatever you want to call it) beyond a year, run as fast as you can if you hear from someone who claims he can predict risk premiums 10 years out, whether reliably or not. It makes zero sense and clearly comes from either a snake oil sales man or an academician with zero experience in and exposure to financial markets/assets.

  • Any financial predictive model, no matter how quantitative, is to be treated with the utmost suspicion and care. Just do your homework: Evaluate the average performance of pure quant based funds vs its peers. You will notice that there is hardly a noticeable difference in performance. I generally am very suspicious of models where the portfolio manager claims the model is a) never overridden and b) is based only on one specific approach, such as fundamental factors or pure technicals. No matter how well a model performs during a specific time span, for example a Bank of Japan currency intervention, a major strike by North Korea, an SEC investigation, a proxy fight, can erase whatever pnl has been built at either an instant or in a very short period of time. The arrogance of steadfastly believing in one's model even in the face of steep unrealized losses has almost always killed such portfolio manager. Sure, you can account for unpredictable events through risk premiums but in the end of the day it does not change the fact: Markets are dynamic and they almost always react to a vast array of factors, almost never does a specific asset trade purely on technical or fundamental factors.

In summary, I really would recommend not to waste time on models that claim they can forecast risk premiums or returns far into the future. None are known to me that outperform risk-free assets (if such even still exist in today's environment). As market practitioner I can assure you that the sweet spot lies somewhere in between ultra high frequency and holding periods of a maximum of a few months. I am not saying there are no investments whose returns materialize in a matter of years but I am talking about holding periods that optimize risk/reward.

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Generally we use models that go so far out in a comparative sense, not as an absolute decision. You are definitely do some good reading but I believe you are thinking about these models in the wrong way.

I think (and correct me if I'm wrong) you are looking at creating or finding the perfect "crystal ball" model that will predict returns/risk premiums etc. for the next 3, 5, 10 years and you make an investment decision based on its output. This is different on how the professional world does it. While generally we wouldn’t use a risk premium model out 10 years we do use these types of models in a comparative sense. We realize it’s impossible to model returns or something like a risk premium so far out so we use these types of models to compare deals not model returns. The models become baselines where we compare the multitude of deals that come across the desk. We don’t say "Hey the model says we will return X yield in 5 years" it’s used like "Hey deal A is X in the model and deal B is Y, why is this the case and which do we like better?"

I think the retail investor is caught up in models as an absolute decision because A) it sounds easy (almost magical, telling the future right?), B) They are looking for one or two "right deals" and don’t see the deal flow and have to do the comparative analysis we do. We HAVE to spend this money (investors looking for returns don’t like it when cash sits around) where retail investors are looking for the right deal.

I hope I'm making some sort of sense. To summarize, in the professional world models help compare similar deals not necessarily model returns. As Freddy said, modeling is often sold to retail investors as a "crystal ball" that can predict not only returns but risk premiums 10 years out (what?!?!). So it doesn’t really matter how you model risk premiums 3-5-10 years (because in reality you can’t) as long as it make sense when used to compare other deals.

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Hi Henry, welcome to the site and thanks for your answer. –  chrisaycock Apr 2 '13 at 15:25

I think Matt Wolf has missed the point. Equity risk premium prediction models actually tend to perform better over longer horizons than shorter horizons. Why this is the case is disputable, however, I think it largely reflects the mean-reverting qualities of equity markets.

With regard to the OP's point about over-lapping time periods, it is OK to us rolling time periods which obviously contain some overlap in observations. What you do need to be careful about is statistical inference based off rolling windows because any independence assumption would be clearly flawed.

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