Standard deviation and 'risk free' investments

[KrazyHorse]

Originally posted by Dauphin


Oh the irony!

Stop being cryptic...

[KrazyHorse]

Originally posted by Vanguard
Which is what you are trying to calculate.

No, it isn't. Calculating a sharpe ratio presumes that you have some sort of idea of both the expected returns of an investment and its expected volatility (specifically, either its variance or the variance of x-Rf).

Sharpe ratios are a way of comparing different investments with different expected returns and different volatilities.

They are not a way of calculating either expected returns or volatilities.

[Dauphin]

Originally posted by KrazyHorse

Also, I find it interesting that you're assuming you know the future development of an investment when the very thing we're after is a statistical quantity dependent on volatility.

Assuming again? I am looking at historic data, and then posed a question of what do you do in the situation where Rf exceeds your returns.

[KrazyHorse]

When did I say I wasn't going to include Rf in the numerator of the sharpe ratio?

I'm arguing about its presence in the denominator.

[KrazyHorse]

Not to mention the fact that you still haven't explained to me how you think a sharpe ratio helps you in making that determination (between Rf and another investment)

[Six Thousand Year Old Man]

Originally posted by Kidicious


There's a risk-free rate. It's the rate that you get from a govt security or something equivilent.

The term is misleading, because of inflation risk, among other things.

[KrazyHorse]

There are a number of risks associated with "risk free". THe real foint is that it is "default risk" free.s

[Provost Harrison]

Originally posted by KrazyHorse


Go bother somebody else, son.

Older than you, lad

[Vanguard]

Calculating a sharpe ratio presumes that you have some sort of idea of both the expected returns of an investment and its expected volatility (specifically, either its variance or the variance of x-Rf).

Yes, of course. But those assumptions about expected returns and volatility are partially based on interest rates. The returns of many investments rise or fall with rates. And unfortunately they do not do so in a simple, direct manner.

Volatility in interest rates does not only affect the investor's borrowing costs. Such volatility also increases or decreases his returns (well, for a large number of investments anyway).

So you can't simply strip the interest rate out of the 'Rf' term, adjust it for volatility, then plug it back in and expect it to be useful. The interest rate isn't built just into 'Rf'. It is also built into 'R'.

So back in the original post, the assumption about interest rates is built into both 'x' and 'Rf'. Which means that the expression

'x - Rf' cannot be used to predict interest rates.

If you want to account for interest rate volatility, calculate the historical volatility of interest rates and plug your adjusted interest rate into the assumptions you make when calculating both return items.

Or just ignore the whole question and generate the ratio in a standardized manner. Whatever. This is way more argument than the Sharpe ratio deserves. Like you, I do not think that the final results are really very useful.

[KrazyHorse]

So you can't simply strip the interest rate out of the 'Rf' term, adjust it for volatility, then plug it back in and expect it to be useful. The interest rate isn't built just into 'Rf'. It is also built into 'R'.

Well, duh.

The point is that if an investment is anti-correlated with interest rates you are DOUBLE COUNTING the effects of volatility in interest rates. This makes sense if you are exposed to upside risk on interest rates, but does not make sense if you are not.

[Kontiki]

Originally posted by Barnabas
In the first world, how widespread is financial speculation (among common people?)

What do you consider "financial speculation"?

[Adam Smith]

Risk-free means no default risk, not constant returns.

The Sharpe ratio is usually used to determine which of several "risky" investments to choose from. In the usual case the default portfolio holding is government bonds, so Rf is the rate for government bonds. However, in the generalized formulation of the Sharpe Ratio, Rf can be any benchmark investment, such as the return on an exisitng investment portfolio that you are considering adding another asset to. In either case it makes sense that negatively correlated assets have a lower Sharpe ratio than positively corelated assets with the same return. The negatively corelated asets are essentially getting credit for reducing the overall variance of the portfolio.

[KrazyHorse]

The negatively corelated asets are essentially getting credit for reducing the overall variance of the portfolio.

Wrong way around. The negatively correlated assets are being penalised.

If deviates a and b are negatively correlated then var(a-b) > var(a) + var(b)

Therefore the denominator is larger, the Sharpe ratio lower and the asset is (supposedly) less attractive.

If you are, overall, a lender at rates tied to bond rates then a negatively-correlated asset will reduce your overall variance. If you are, overall, a borrower then it will increase your variance. Vice-versa with positively-correlated assets.

In other words, if I have a portfolio of short-term government paper and want to sell a small amount to purchase another asset, then Sharpe ratios will tell me to prefer assets which are positively correlated with interest rates compared with those which are negatively correlated, but in reality I should prefer assets which are negatively correlated.

[Vanguard]

Ok, if the question is just "should I use Sharpe or should should I use Sortino", then never mind. Forget I said anything.

I thought Dauphin was looking for a way to account for interest rate swings larger than those in the given data.

[Adam Smith]

Originally posted by KrazyHorse
Wrong way around. The negatively correlated assets are being penalised

Oops. Thought the -'s were +'s. If so you get the returns for two streams of assets combined
E(Ra + Rb)/SD(Ra + Rb) = 1/CV(Ra + Rb), which works properly since
VAR(Ra + Rb) = VAR(Ra) + VAR(Rb) + 2COV(Ra,Rb)

But that's not a Sharpe ratio