Structural Beta and Alpha

In a recent refresher of Dalio’s interviews, I came across a term he mentioned: “Structural Beta.” What is it and what insights can one gain from this concept? I went on to do some research and reading on the subject and here are a few things I found.

Beta defined by the CAPM is the slope of the linear regression between the Market Return (symbol) and the securities return. The measure takes in to account both the covariance (correlation) and the standard deviations. Mathematically,

Where subscript ‘a’ represents an asset and ‘m’ represents the market. From the above equation, we can see that there are two determinants to the value of beta.

1. market volatility

2. correlation between market and asset

With the above determinants, it is intuitive to note that although an asset may have low correlation, offering potential diversification benefits, it may still poses equal beta due to the volatility of its underlying returns.

There are two things that are important when constructing a portfolio, the return and risk. Return can be improved and risk can be reduced if a historically lowly correlated asset is added to the portfolio. But there are times like 2008 when things don’t follow historic averages. What I mean by this is that there can be assets that have low correlation but also high volatility. As an alternative, Beta can be used to gauge both of these characteristics. In a portfolio level context, beta may be used as an alternative measure of portfolio risk as it offers more information (correlation, volatility) than volatility alone in the traditional sense.

There are numerous different ways to measure portfolio risk and these metrics are used on a daily basis as ingredients to portfolio optimization that yields weights for portfolio allocation. But these simplistic measures, ie volatility, may mislead as it may potentially hide the true risk inherent inside the portfolio.

The chart below is a traditional Standard deviation based risk return graph. The expected returns are probably not representative as I just have 24 years of total return data; but I am confident the concepts are preserved.

Standard_RRThe next chart is through the beta lens whereby risk is measured by beta rather than standard deviation.

beta_risk-return

The blue lines in both charts are called the cash equity line while the horizontal line merely represents the risk free rate (proxied by SHY). If an asset is above the cash equity line, than the area inbetween the asset and the line represent what is called structural alpha. This type of alpha is not the typical alpha that is generated by skill; rather it is the return portion that is attributed to an asset itself. It offers great diversification benefit to a portfolio. The beta based return is the portfolio above the risk free line and below the cash equity line. This portion of return is theoretically replicable by a mix of cash and equity.

All in all, this view of portfolio risk return may warrant more research, for example, what happens when we long a portfolio of assets that show structural alpha? It is also important to note that in the past two decades, the assets that have shown to have diversification benefits all evidently lie above the cash equity line in the beta risk return chat. For example, the success of permanent portfolio was attributed to holding such assets.

Code for generating risk return given xts object. Package: PerformanceAnalytics, SIT

gen.risk.ret<-function(data1){
 data1<-as.xts(data1) #convert to xts
 ret<-get.roc(data1,1)
 returns<-compute.cagr(data1)
 risk<-apply(ret,2,sd)
 risk.ret<-cbind(risk,returns) #Standard Risk Return Matrix
 return(risk.ret)

}

gen.beta.ret<-function(data1,bm){
 data1<-as.xts(data1) #convert to xts
 ret<-get.roc(data1,1)
 returns<-compute.cagr(data1)
 bench<-ret[,which(colnames(ret) == bm)]
 risk<-matrix(NA,nrow=1,ncol=ncol(ret))
 for(i in 1:ncol(ret)){
 risk[,i]<-CAPM.beta(ret[,i],bench,Rf=0)
 }
 risk.return<-cbind(as.vector(risk),returns)
 rownames(risk.return)<-colnames(ret)
 colnames(risk.return)<-c("beta","returns")
 return(risk.return)
}
Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s