How can negative beta might occur even when both the benchmark index and the stock under consideration have positive returns ?
This is very simple, actually. All you need is for there to be a negative correlation for the beta to be negative.
Remember, one way to express beta is (STDEV of Asset A / STDEV of Benchmark)*Correlation of Asset A & Benchmark.
So, suppose the standard deviation of Asset A is 10% and the standard deviation of the Benchmark is 5%. If the correlation between the two time series is -0.5, your beta will be -1.
Note that this formula requires no inputs regarding returns - all that matters is the reference standard deviations, and the correlation between the two references.
Does that seem clearer?
What you have explained is clear. But my actual confusion is, How can correlation be negative when both bench mark return and stock under consideration have positive return?
If both price series have an upward trajectory, but happen to move opposite each other on their upward march, then the price series will have negative correlations with each other, even though the prices of both the stock and the benchmark finished higher than where they started.
Beta/Correlation tracks the co-movement of an asset with market/benchmark. If the movement of the asset is mostly opposite to the benchmark, creates negative beta. Thought the expected return for both can be positive. Hope it makes sense?
I got your point, but still not clear how Beta can be negative when both stock and benchmark have positive returns. It will be helpful, if you state by using an example.
Gold is often talked as negative beta or a hedge against inflation, recession.
If beta is negative and expected return of the market is positive, it means theoretically your asset will earn lesser return than risk free return.
There are stocks with negative regression betas, but those are the mostly the result of something strange happening during the period of the regression - an extended lawsuit or acquisition battle throwing off the correlation with the market- rather the true betas.
Thanks
If I had more time, I could come up with a better example, but this should suffice, for now.
Put the following in an Excel spreadsheet, in two columns: Returns for Stock A = 4%, 10%, -2%, 7%, -3%. Returns for Benchmark = 0%, -1%, 12%, -2%, 5%.
Calculate the standard deviation of each one; you will find that the STDEV of Stock A equals 5.6% and the STDEV of the Benchmark equals 5.8%.
Next, calculate the correlation between the two. You will find that it equals -0.82. Using the formula I described in my earlier response, this means beta equals (5.6/5.8)*-0.82 = approximately -0.80.
You will notice that the average return of the Stock A series is positive (3.2%) – and so is the average return of the benchmark (2.8%). Also note that the total compounded return for both over the 5 periods is about 16% for Stock A and 14% for the Benchmark.
In other words, no matter how you slice it, in this scenario, both Stock A and the Benchmark exhibit positive returns, yet are negatively correlated; thus, you get a negative beta for Stock A. This is absolutely possible, and I hope that my example proves to you mathematically that this is the case.
My Pleasure
Yes as per perfectly described by Destroyer of worlds beta can be negative in the case the average return is positive and similar.
Bear in mind that correlation (of returns) describes one asset’s returns relative to its average compared to another asset’s returns relative to its average. If both have positive average returns, but one is above its average when the other is below its average (and vice versa), they will have a strong, negative correlation of returns, even though both (always) have positive returns.
Many people in finance mistakenly believe that negative correlation means that one is positive when the other is negative. This is, well, wrong.