Can portfolio risk be reduced to zero? question, stocks, across, should

nixie24

Came across this interesting question.
Unsytematic risk- If choose 1000 stocks, it will be zero
Systematic risk- If choose a portfolio with zero beta, then systematic risk should be zero.
Therefore, I conclude that portfolio risk can be reduced to zero. What am I missing here?

RobertA

It’s only possible if you hold 100% the risk-free asset.
My personal portfolio has a beta of 0.013 and its volatility is still about 8% (compared with about 23% on the S&P500.)  Zero beta only implies a lack of correlation with the S&P500, not a lack of risk (or volatility.)

Iginla2010

Systematic risk can be zero if you have truly zero beta. So, statement 2 is correct. The problem is that a zero beta asset probably does not exist. If Godzilla destroys New York, most likely, all asset classes will be affected. That is, they are all correlated in extreme events.

Finalnub

Beta is far from perfect, so no you cannot have a zero risk portfolio.

hariRaj

Ok, whatever. It’s not really material to distinguish zero beta assets from zero beta portfolios. If you could build a zero beta portfolio, you could just package that into shares and create a zero beta asset. The point (as everyone is saying) is that true zero correlation is not achievable.

king_kong

thanks a lot.
Anyone remember the name of a stock having different beta at different market condition (e.g. 0.5 in down market and 1.5 in up market)?

ba736

^ if I knew of a stock with a 0.5 beta in down markets and 1.5 in up markets, I wouldn’t be at work right now, I’d be telling my butler to get me another beer.

lunarfollies

maisatomai wrote:
thanks a lot.
Anyone remember the name of a stock having different beta at different market condition (e.g. 0.5 in down market and 1.5 in up market)?
Beta is going to be symetrical because its the slope coefficient that minmizes the squared errors, the example above would have a beta of 1.0 because the errors have to be symmetrical.
Regarding the portfolio with zero risk, you can do it with options to grow at RF- but you’d be taking on counterparty risk. Best bet is 100% treasuries as someone said.
my 2 cents (to the best of my knowledge)

giants2010

maisatomai wrote:
…I conclude that portfolio risk can be reduced to zero.
In theory, all you need is two perfectly negatively correlated assets. Set w1=sigma2/(sigma1 + sigma2), and you have a zero volatility portfolio. Again, assuming corr1,2 = -1.
As per the zero beta portfolio, it can also be easily achieved with index futures. Counterparty risk should be minimal.