# Is systematic risk that non-diversifiable?

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Yikes. Having a beta of 1 does not mean that you have gotten rid of diversifiable risk. I can take any stock and with the right combination of leverage or risk-free paper get a portfolio with beta of 1 that contains tons of diversifiable risk.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

I didn’t say that if beta=1 there’s no diversifiable risk. All I said is that it seems possible to diversify away non-diversifiable risk (measured by beta).

” diversify away non-diversifiable risk” huh? The definition of non-diversifiable is that you can’t diversify it away.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Beta measures systematic risk (i.e. marlet risk, diversifiable risk) can be reduced using diversification.

Idiosyncratic (i.e. non-systematic risk, company specific risk, non-diversifiable risk) cannot be reduced using diversification.

Olivier Wagner

Olivier, it’s the other way.

Systematic risk is the risk inherent to the entire market and it’s non-diversifiable.

Unsystematic or company specific risk can be diversified.

cfa_moscow, it’s not about beta, it’s about deviation from the market component. In other words, it’s about correlation not beta (beta = correlation*sigma_portfolio/sigma_benchmark). The higher the correlation, the smaller the unsystematic component.

We are rewarded for taking on market risk because it is non-diversifiable. Company specific risk (residuals of CAPM) can be eliminated by diversification hence no reward for this risk

maratikus Wrote:

——————————————————-

> Olivier, it’s the other way.

>

> Systematic risk is the risk inherent to the entire

> market and it’s non-diversifiable.

>

> Unsystematic or company specific risk can be

> diversified.

>

> cfa_moscow, it’s not about beta, it’s about

> deviation from the market component. In other

> words, it’s about correlation not beta (beta =

> correlation*sigma_portfolio/sigma_benchmark). The

> higher the correlation, the smaller the

> unsystematic component.

Crap. You are absolutely correct. And I am absolutely sleepy :)

Olivier Wagner

Guys,

all you are talking about are just formal definitions.

But beta is the measure of systematic (non-div.) risk. But if we add to portfolio stock with lower beta the new total beta would be less than before addition of the stock. So as the beta is the measure of systematic risk => there will be less systematic (non-div.) risk in new portfolio. Therefore we can diversify non-diversifiable risk.WTF??

Can anyone explain where I’m wrong?

In this context, most of us only use the term diversify to refer to removing uncompensated risk. We can arbitrarily choose the beta of our portfolio, but reducing it also means reducing our return. Diversification strategy is about minimizing risk for a given level of return.

you need at least 19 stocks to diversify about 95% of firm specific (unsystematic) risk.

From mean-variance persepctive, diversification means you can get the same return with lower variance. A lower portfolio beta indicates a low risk-adjusted return arising from the addition of a new stock with a lower beta. In other words, your portfolio variance may be reduce but same applied to your return. Bottomline, there is no reduction on your overall systematic risk. You are just willing to accept a lower return by having a low risk (variance) in your portfolio.

cfa_moscow, think about systematic/unsystematic risk in terms of linear regression where market index is the independent variable and the portfolio is the dependent variable. Portfolio gets decomposed to its systematic component through beta and the rest is the unsystematic component: P = beta*M + Res. Linear regression R^2 is the ratio of variance explained by the systematic component to portfolio variance. R^2 = beta^2*Var(M)/Var(P). It’s obvious that the higher R^2, the smaller the RELATIVE weight of the Residual (unsystematic) component. Since R^2 = correlation(P,M)^2, the higher absolute value of correlation, the higher R^2.

By the way you can get rid of systematic component, if you use a market neutral strategy. Buy one stock, sell another stock in certain proportion. Then your systematic risk is zero, and all your risk is unsystematic. Such portfolio in some sense is least diversified since all your risk is unsystematic or dependent on stock picking.

cfa_moscow, where do you get the idea that beta is addible? I have never heard of such theory.

beta= covariance between the asset and market return / variance of market return

If you created a new portfolio, you need to find the covariance of the portfolio with the market, in order to find the portfolio beta. You cannot just take the weighted average of the beta.

Hmm….I hear this for the first time. According to theory, the portfolio beta is indeed just the sum of the individual stock betas multiplied by their respective portfolio weights.

Also, what maratikus described is a well-known hedge fund strategy called relative value trading, where it is in fact possible to end up with a portfolio beta of zero. You make a bet on a pair of stocks and you do not want any exposure (read market) except for the one that they have to each other.

Diversification is equivalent to: I can get a higher return for the same risk OR a lower risk for the same return. Reducing my portfolio beta would not achieve this, as many have stated above…

OK, so explanation that diversification is reducing risk for GIVEN return sounds very reasonable. Then reducing beta is not diversification as the return would also go down. But adding more and more stocks with the same beta (for example) to portfolio will reduce risk by diversifying away unsystematic component, keeping required and expected return at the same level.

Thank you guys.

Beta is a risk measure against benchmark you choose like market index. If beta is 1, it means that your portfolio has the same risk as market risk, nothing to do with risk free.

Khalix Wrote:

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> Beta is a risk measure against benchmark you

> choose like market index. If beta is 1, it means

> that your portfolio has the same risk as market

> risk, nothing to do with risk free.

No it doesn’t mean that. For example, a single stock portfolio could have a beta of 1 and would have more risk than the market. A stock can have a beta of 1 and correlation with the market darn close to 0 and have very high variance.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!