Can portfolio risk be reduced to zero?

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maisatomai

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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?
 
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.)
 
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.
 
Beta is far from perfect, so no you cannot have a zero risk portfolio.
 
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.
 
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)?
 
^ 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.
 
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)?
Click to expand...
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)
 
maisatomai wrote:
…I conclude that portfolio risk can be reduced to zero.
Click to expand...
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.
 
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)?
Click to expand...
Convertible preferred’s?
 
Beta of zero implies that a portfolio’s systematic risk can be pulled to zero. Of course, a beta of zero may not be reliable in practice, particularly in extreme events.
However, a portfolio with a beta of zero will still have some non-systematic risk or tracking error. If you have a 1000 stock portfolio, that tracking error is likely to be very small, at least if the asset weights match the benchmark’s portfolio’s. At that point, the question is why you wouldn’t just hold cash/treasuries. The answer is that you might hold the portfolio in normal times and just neutralize it if you think that the short term forecast suggests substantial downside risk for a short time.
 
Create all the zero beta portfolios you want, but unless you’re netting out to no position at all, you’re definitely not going to have a fully explanatory model (R^2 < 1). I’ll never get over people talking about the beta of a stock/portfolio and trying to make investment decisions when its R^2 against the relevant index is like 0.2.
But no, the OP is right, take any combination of stocks with weights that provide an estimated beta of 0, and suddenly you’re making riskless profit…
 
Unless your decisions on portfolio weights are adding value, a zero beta portfolio is most likely to generate zero profit as well. In my view, the point of producing zero beta is to be able to separate the comparative analysis portion (company vs company) from the macro-systemic risk-return.
 
Someone mentioned futures on indexes. I don’t think derivatives count when defining “total market” or “tradeable assets”, whatever that is. (But it ain’t derivatives, but I don’t know what it is :))
Would you say this is a zero-risk portfolio: 1 call + 1 put on the same stock, at the same asset price? Or 3x Bull + 3x Bear ETFs? For options, you’re paying the time premium even if they move in perfect tandem. For ETFs, ETF fees.
 
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