Standard deviation and 'risk free' investments

[Dauphin]

e.g You borrow at fixed 4%, the investment pays a stable 5%, with minor fluctuations. Rates increase to 6% over a period. Would you retain your investment if you could sell them and make 6% on a deposit for the remainder of your loan term?

[Provost Harrison]

I think KH it is time you relegated yourself down your own league table. It is quite evident to everyone else that you have been pwned

[Six Thousand Year Old Man]

Ain't no such animal as a risk-free investment.

[Vanguard]

I just don't see what the problem is. Calculate the ratio for each investment. Pick the higher one.

[KrazyHorse]

Originally posted by Dauphin


You have made two assertions which are false already, I'm not overly confident in your latest assertion.

Whilst you may be shielded from interest rate changes on borrowings or investments I am not convinced that you can ignore the local risk free rate in favour of your personalised risk free rate as the fixed personalised rate you can get at any instant will vary with the risk free rate.

Yes, but so what? Unless you're borrowing to invest (or are investing while in some other sort of debt...though I don't know why you would do this except with a mortgage, which is often fixed-rate) then what does this have to do with the price of tea in china?

[KrazyHorse]

Originally posted by Provost Harrison
I think KH it is time you relegated yourself down your own league table. It is quite evident to everyone else that you have been pwned

Go bother somebody else, son.

[KrazyHorse]

Originally posted by Vanguard
I just don't see what the problem is. Calculate the ratio for each investment. Pick the higher one.

Again, it depends on what you're doing. If you borrow money to invest at a variable rate then you need to be aware of the spread between your return and the amount of interest you are paying on your loan.

If you are not exposed to fluctuations in interest rates then why the hell would you include them in your calculation?

[Kuciwalker]

Originally posted by KrazyHorse
Unless you're borrowing to invest

See post #19.

[Kidlicious]

Originally posted by Six Thousand Year Old Man
Ain't no such animal as a risk-free investment.

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

[KrazyHorse]

Originally posted by Dauphin
e.g You borrow at fixed 4%, the investment pays a stable 5%, with minor fluctuations. Rates increase to 6% over a period. Would you retain your investment if you could sell them and make 6% on a deposit for the remainder of your loan term?

I do wish you would think about what you're saying. Plug in Rf as your x in a sharpe ratio and tell me what the result is. 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.

The comparison has to be the following:

Say you borrow at 4% steady.

After one year the market rate rises to 6%, but you are insulated from the cost of borrowing.

Investment A pays off at 10% the first year and 15% the second. Investment B pays off at 15% the first year and 10% the second.

The sharpe ratio for A would be (doing arithmetic means):

E(x-Rf) = 0.5(0.1+0.15) - 0.5(0.04+1.06) = 0.075

var(x-Rf) = 0.5(0.1-0.04)^2 + 0.5(0.15-0.06)^2 = 0.00585

For B,

E(x-Rf) = 0.075 (again)

var(x-Rf) = 0.5(0.15-0.04)^2 + 0.5(0.1-0.06)^2 = 0.00685

So SA = 0.310
SB = 0.287

Now, if you have money borrowed at a variable rate, then A makes sense as a better investment, because you are hedging your interest rate risk.

But what if, for example, you have money LENT at a variable rate? Now you're INCREASING your overall variability for the same expected returns.

Whether or not you should take Rf into account in calculating your variance depends entirely on your overall exposure to interest rates. In some cases, an investment which hedges against fluctuations in rate changes is a good idea relative to one which does not, even given identical expected returns.

The sharpe ratio is an oversimplified piece of garbage.

[Barnabas]

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

[KrazyHorse]

I don't know. My plan is simply to dump money into index funds...

[Vanguard]

Again, it depends on what you're doing. If you borrow money to invest at a variable rate then you need to be aware of the spread between your return and the amount of interest you are paying on your loan.

If you are not exposed to fluctuations in interest rates then why the hell would you include them in your calculation?

Well, the only use for a Sharpe ratio is to compare it to other Sharpe ratios. Doing so allows you to compare investments with different volatility risks.

But you can't include borrowing costs into this ratio because borrowing costs depend on the risk of the investment and its rate of return. Which is what you are trying to calculate.

[Dauphin]

Originally posted by KrazyHorse


I do wish you would think about what you're saying.

Oh the irony!

[KrazyHorse]

Originally posted by Vanguard
But you can't include borrowing costs into this ratio because borrowing costs depend on the risk of the investment and its rate of return. Which is what you are trying to calculate.

What the **** are you talking about?