 # Mean reversion analysis

• Suppose that a manager believes that credit spreads are mean reverting. Below are three issues along with the current spread, the mean (average) spread over the past six months, and the standard deviation of the spread. Assuming that the spreads are normally distributed, which issue is the most likely to be purchased based on mean-reversion analysis? Issue** Current Spread Mean Spread for Past 6 Months Standard Deviation of Spread** A 110 bps 85 bps 25 bps B 124 100 10 C 130 110 15
• What are the underlying assumptions in using mean-reversion analysis?

A. 25bps can pickup.

Underlying assumption: Converge to long-term average.

Frank,

This a table already given. This is a EOC Q and it does not make sense to me. The answer has a formula whih does not show up anywherein the text. I am confused.

My previous answer miss the volaitility part Need to divide the standard deviation to make a comparsion.

The concept is simliar to Sharpe ratio and Roy’s Safety-First Measure.

That’s exactly my point. Why divide by std?

Think: why Sharpe ratio and Roy’s Safety-First Measure divide by std?

To adjust the return on risk basis- per unit of risk

Exactly. Same here. Portoflio management always need to look at risk.

Thanks Frank.

You are welcome.

Another (and more statistical) approach to your question is this: if we standardize the current value for each (subtract off the mean and divide by the standard deviation), we can see which asset is currently the furthest away from its mean (in terms of standard deviations). The one with the largest standardized value is most “unusual” and is more likely to revert towards its mean (they said its mean reverting), since it’s the farthest away.

Plain and simple: You know that the series is mean reverting, so the further away from the mean you are (in terms of standard deviations), the more likely it is that you’ll be heading back that way. Pick it up before the spread contracts.

B) since it has the highest standard deviation away from the mean (2.4 away from mean)

For selling a bond, I guess you would have a negative number since current spread would be lower than historical spread but you would still choose the bond with the highest ABSOLUTE standard deviations away from the mean

SELL?

SELL?

SELL?

WHAT THE F…

Ummm why is sell even being mentioned here ? I made a boo boo if so

for selling, i would think it’s the lowest value of (current-mean)/standard deviation as those would have the least price gain from spread reverting to mean.

i agree with jmsp and Patso…yea SELL not BUY.

I need a hug Based on mean reversion analysis, my guess would be to sell the bond with the lowest spreads deviation from its mean, which is A?

The other bonds with more deviation will see their spreads come back down to their mean, which results in their prices going up - so why would you sell them if their prices will go up more, compared to the one that’s sitting around its mean?