Harvesting Risk Premia

NBIM from Norway have a nice summary of the main market anomalies discussed on this blog:


The anomalies are size, value, momentum and volatility (beta).

Excess annual returns from value, small cap and momentum are 4%, 3% and 8% respectively:


While the low beta out-performance has been about 4%.


Returns for the 4 factors over the last 2 decades are also displayed graphically, with all except Value contributing to the current bull run.  Notice the large “momentum crash” during the last recession.


The paper also covers integrating the factors for a large portfolio (pension fund).  It is well worth reading for an overview on how professional money managers approach fund design.

Recession models: walk forward testing

One common criticism of recession models is that they are back-fitted and therefore unlikely to continue working in real time.

RecessionAlert has an interesting walk forward analysis of their recession model, demonstrating robustness:


We achieve this by simulating a person sitting in December 1968, right before the second recession shown on all the above charts and attempting the optimization on known co-incident data to that point. We then project that model into the future to present day to see how it would have continued to perform in “out of sample” data … We repeat again including data to the 4th recession, 5th recession and so on …

We make several remarkable discoveries from the tests. The first model built hypothetically in 1969 using data from 1st July 1959 through to Nov 1969 and encompassing one recession and expansion (red line in above chart) continued to perform remarkably well into the future. Remember, once this model was constituted in November 1969, it was never modified or altered.

The second important observation is that there is not much difference between the 1st model and the 6th. Continue reading

Exploring model parameters (not curve-fitting)

The basic model buys the fund with highest one year price change (ROC252) after an intermediate correction (>1% US stocks down 25% in one month).

It is instructive to see the effect of “hold time” and “severity of correction” on returns.  Generally, deeper corrections provide faster returns but occur less frequently.  Two thirds of the returns are captured with a simple 2 month hold (over the last 10 years) and less than 50% exposure.  This underlines the importance of the capturing the rise from intermediate lows.

(Testing over a longer period is more difficult due to lack of breadth data).

Amibroker code is shown at the bottom of the post.

blog figs

Most combinations of hold time and pullback severity give annual returns above 24%.  The results at the back corner of the plot (short hold and deep pullback) have higher risk adjusted returns and Sharpe but lower overall returns due to lower exposure (see next 3 plots).

blog figs

blog figs

blog figs

Interestingly, testing the strength of the breadth thrust for entry with a fixed hold time showed little effect.  Therefore, the key strategy is to buy momentum at an intermediate low and hold around 6 months to capture the bulk of the returns.  The recession filter is also active.  This is important to avoid buying into “waterfall” declines.


Buy =   r_filt AND d1>=Optimize(“d25%”,1,0,2,0.5);

Sell =  0;

PositionScore = IIf(ROC(C,252)>0 , ROC(C,252),0);