?p=25675

One Stock _beta_ Value usually means its relationship with the market , When the market changes 1% when , What percentage change do we expect in the stock .

market , It's a somewhat vague concept , As usual , We use standard & Poor's 500 Approximate calculation of the index . The above relationship （ hereinafter referred to as β） It is detrimental to many aspects of trading and risk management . What has been determined is , Volatility has different dynamics for rising and falling markets . We have to use regression to estimate beta anyway , So for investors who want to fit this asymmetry , Piecewise linear regression is appropriate .

The idea is simple , We divide the data set into two （ Or more ） part , And separately 、 Block by block or _ piecewise _ Estimate each part . This simple idea can be implemented with complex symbols and code .

To illustrate , I use Microsoft Stock market yield data (MSFT).

I have estimated different rates of return β value , The positive sun is above zero , The negative day is below zero , So zero is our breakthrough point .( This breakthrough is known in academic terms as " junction ", Why " junction " Well ？ Because it connects the two parts .) The following figure shows the results .

getSymbols




for (i in 1:l){

dat0 = getSymbols

rt\[,i\] = dt\[,4\]/dt\[,1\] - 1

}

lal = lm

plot abline

Maybe β The value is always the same , Until the extreme negative value , Only when the market drops sharply , Relationships change . This belongs to the category of structural change . I think about the grid of points along the axis , And build a model , There is a breakpoint at each point , There is a slope before the breakpoint , There is a slope after the breakpoint . I find the minimum value of the sum of square errors of the whole sample , So I add the squared errors of the two models . The figure below shows the result .

plot(ret\[,1\]~ret\[,2\]
segments
grid1
grid2 

##  Note that there （ret\[,2\]<grid2\[i\]）, It's an index function 


for (i in 1:length(gid2) ) {
rneg <-lm
rpos <-lm
d\[i\]<- summary
}
plot
text
points

Grid search on the optimal model

ok , The data is not zero , But almost zero , Bad luck , All this work , What do I ask you ？ ok , In order to use the correct _ Beta _ , All you have to do now is decide whether it is a bear market or a bull market ...... It should be easy . Thank you for reading , The code is as follows .

data display , Node is not zero , But almost zero , In order to use the correct β value , All you have to do now is decide , Is this a bear market or a bull market , Thank you for reading .