# The Duration Factor

**Read the paper on SSRN**

**Abstract:**

John Rae’s inter-temporal choices explained the statistical nature of human behavior in 1834. However, despite the subject’s insight in the objectiveness of behavior, inter-temporal choices remains a peripheral science. This paper takes a sequential approach to question how inter-temporal choices could be behind human behavior, behavioral anomalies and even market anomalies. If these inter-temporal anomalies were consistent, unarbitrageable and explain asset returns better than the Fama and French Factor model, this could further our understanding of asset pricing models by establishing a new duration factor which could subsume both size and value factors.

What’s a duration?

It is how long one holds an asset; time till a decision is made; time between events.

How is it connected to inter-temporal choice?

Inter-temporal choice was a subject coined by John Rae in 1834, which explained how we made choices in different points of time.

Why is inter-temporal choice important and how is it related to natural systems?

It forms the basis of decision making and is connected to a discount rate. It proves that decision making based on duration is mathematical, as we discount future more than the present. It challenges the idea of subjective behavior over quantifiable behavior. Natural systems are quantifiable and behavior is driven by a natural system. The system works on reversion, which is statistical. The system works on divergence (noise, fluctuation, error, anomaly), something to revert.

So where does behavior come in?

Modern behavior studies accept reversion as a law, but consider divergence owing to human behavior. So if we assume, that diversion (noise, fluctuation, error, anomaly) was behavioral and behavior was driven by mathematical duration, then divergence should also be mathematical.

So there is more objectivity than subjectivity?

Yes. In simple terms, if humans discount future more than the present, consistently than behavior is subsumed by statistical duration, which makes behavior objective and statistical.

So, this means, it’s not a behavioral anomaly, but an inter-temporal anomaly?

Exactly. Behavioral anomalies are owing to inter-temporal choices, so subjective behavioral anomaly is an expression of inter-temporal anomaly.

This means, even investing and inter-temporal anomalies are connected?Investing is not just connected with inter-temporal anomalies, but duration drives investing. Even if Value is an important investing style, there are more takers for growth. Value is longer term and Growth is shorter term, as we discount longer term value more that shorter term growth.

This is why, markets work in a cycle of reversion and diversion?

Human inter-temporal discounting behavior drives divergence, extremities, creating bubbles which invariably revert creating cycles; as growth diverges far away from value; markets revert and then the cycle repeats. Yes, behavior is mathematical like everything else.

What about modern finance? Does Inter-temporal choice influence that too?

The 1960 CAPM Nobel, assumes temporal independence. It is a static linear model which assumes that past does not affect the future. The asset returns of ‘today’ and its sensitivity to market ‘today’. While serial correlation, temporal dependence, over longer duration is know to be valid, is confirmed, it works, it is an observed fact.

What does this mean for Finance?

It means that finance sees two behaviors. On one side it accepts temporal dependence over longer term, but simplifies dynamic non-linear systems in a linear temporal independence equation. Simply putting, modern finance accepts duration, but does not know reconcile the temporal independence and dependence in a pricing model.

Is it important to reconcile?

Yes; if it explains asset performance better; gives risk-weighted excess returns; and does not get arbitraged away, we have a new pricing model for the industry.

How will this model will look like?

Let’s look at investing behavior. Value works for longer term. Momentum (growth) is shorter term compared to value. So if value and growth were statistical concepts then value and growth would be comparable. And if they were comparable, they could be built as a factor.

You mean like the Fama and French, Size and Value factor?

Yes. One could look at statistical value minus statistical growth as a factor which could subsume Fama and French factors and other factors.

What would one see in such a statistical Value-Growth pair?

One would see that value longer term – growth shorter term would generate a premium. And this premium would not be arbitrageable, as it is centric to inter-temporal anomaly.

This is how we explain investing with inter-temporal anomaly?

Correct. At Orpheus we call it the ‘duration factor’, the longer term statistical value – shorter term statistical growth premium i.e. RMI Value – RMI Growth premium. For us both value and growth are statistical and value is longer term and growth is shorter-term (compared to value).

A redefinition of CAPM and Fama and French factor model.

Yes. If this duration factor subsumes size and value factors, the anomaly should be consistent, unarbitrageable and explain asset returns better than the Fama and French Factor model.

The Sociological Theory of Capital, Rae (1834)

Behavioral Finance, Thaler, (1999)

Temporal Changes in Shiller’s Exuberance Data, Pal, Mitroi, Shah (2011)

Is Smart Beta Dumb? Pal, (2015)

Mean Reversion Framework Pal, (2015)

Momentum and Reversion, Pal, (2015)

Stock Market Stationarity, Pal, Ferent, (2015)

Arbitraging the Anomalies, Pal, (2015)

Is Reversion Statistical? Pal, (2105)