Standard deviation and 'risk free' investments

[Dauphin]

If you have a liquid investment that gives a variable return of x per month, you can work out the standard deviation over a year in a straight forward manner.

If you have a fixed rate of risk free investment Rf, the standard deviation of x won't change when calculating the return relative to a risk free investment, x - Rf.

My question is this, if Rf is volatile over the year, is it more sensible to calculate the geometric average Rf, thus keeping standard deviation of the returns of your investment fixed regardless, or is it more sensible to calculate the standard deviation of the variable x - Rf?

My gut says that you shouldn't be measuring the standard deviation of interest rates when considering an investment's deviation, but logic tells me that there is downside risk or upside potential when rates increase or decrease even if your returns of x are fairly stable and so they have to be included.

If anyone is interested I am looking at Sharpe and Sortino ratios.

Cheers.

You can all go back to sleep if you aren't, as is likely, interested.

[lord of the mark]

Re: Standard deviation and 'risk free' investments

Originally posted by Dauphin
If you have a liquid investment that gives a variable return of x per month, you can work out the standard deviation over a year in a straight forward manner.

If you have a fixed rate of risk free investment Rf, the standard deviation of x won't change when calculating the return relative to a risk free investment, x - Rf.

My question is this, if Rf is volatile over the year, is it more sensible to calculate the geometric average Rf, thus keeping standard deviation of the returns of your investment fixed regardless, or is it more sensible to calculate the standard deviation of the variable x - Rf?

My gut says that you shouldn't be measuring the standard deviation of interest rates when considering an investment's deviation, but logic tells me that there is downside risk or upside potential when rates increase or decrease even if your returns of x are fairly stable and so they have to be included.

If anyone is interested I am looking at Sharpe and Sortino ratios.

Cheers.

You can all go back to sleep if you aren't, as is likely, interested.

Im vaguely interested, but havent really thought about this stuff for over 20 years, and will wait for others to reply.

[Grandpa Troll]

Re: Standard deviation and 'risk free' investments

Originally posted by Dauphin
If you have a liquid investment that gives a variable return of x per month, you can work out the standard deviation over a year in a straight forward manner.

If you have a fixed rate of risk free investment Rf, the standard deviation of x won't change when calculating the return relative to a risk free investment, x - Rf.

My question is this, if Rf is volatile over the year, is it more sensible to calculate the geometric average Rf, thus keeping standard deviation of the returns of your investment fixed regardless, or is it more sensible to calculate the standard deviation of the variable x - Rf?

My gut says that you shouldn't be measuring the standard deviation of interest rates when considering an investment's deviation, but logic tells me that there is downside risk or upside potential when rates increase or decrease even if your returns of x are fairly stable and so they have to be included.

If anyone is interested I am looking at Sharpe and Sortino ratios.

Cheers.

You can all go back to sleep if you aren't, as is likely, interested.

I deal with standard deviations in relationship to performance of concrete mixes, in relaionship to what your saying, if I had "X" which had a liquid or "fluctuating" return of data vs a more "fixed" which by that I mean a more stable, than I would tend to want to place my chips on the known or "fixed" data.

I just feel "fluctuating" or "liquid" is just that, not as stable and most certainly not predictable.

For a higher ROI one could argue over the lifetime of an investment either would do well, but then again thats based on "historical" and most certainly not "potential" R O I.

I tend to play it safer and more steady, over the long haul go with what is known.

It is known, that some "fluctuating" investments do just that, how high is the high may not be the question, making extra os great, the real question is how low is the low, as in losing all you have invested.

Gramps

Not an investment/economic's major, just a simple business manager for over 20 years

GT

[Japher]

if your returns of x aren't very variable then who cares? create another metric that measures the rate of variability of the variable interest (second order, unitless) to benchmark against and determine a risk factor off of that, which will tell you when it would be safer to use one equation over the other. Because, if Rf is volatile, how volatile? Would it greatly influence the variability of x? Either that or I'd always go with x-Rf

[Provost Harrison]

Re: Standard deviation and 'risk free' investments

Originally posted by Dauphin
If you have a liquid investment that gives a variable return of x per month, you can work out the standard deviation over a year in a straight forward manner.

If you have a fixed rate of risk free investment Rf, the standard deviation of x won't change when calculating the return relative to a risk free investment, x - Rf.

My question is this, if Rf is volatile over the year, is it more sensible to calculate the geometric average Rf, thus keeping standard deviation of the returns of your investment fixed regardless, or is it more sensible to calculate the standard deviation of the variable x - Rf?

My gut says that you shouldn't be measuring the standard deviation of interest rates when considering an investment's deviation, but logic tells me that there is downside risk or upside potential when rates increase or decrease even if your returns of x are fairly stable and so they have to be included.

If anyone is interested I am looking at Sharpe and Sortino ratios.

Cheers.

You can all go back to sleep if you aren't, as is likely, interested.

My answer is yes.

[KrazyHorse]

Re: Standard deviation and 'risk free' investments

Originally posted by Dauphin
If you have a liquid investment that gives a variable return of x per month, you can work out the standard deviation over a year in a straight forward manner.

If you have a fixed rate of risk free investment Rf, the standard deviation of x won't change when calculating the return relative to a risk free investment, x - Rf.

My question is this, if Rf is volatile over the year, is it more sensible to calculate the geometric average Rf, thus keeping standard deviation of the returns of your investment fixed regardless, or is it more sensible to calculate the standard deviation of the variable x - Rf?

My gut says that you shouldn't be measuring the standard deviation of interest rates when considering an investment's deviation, but logic tells me that there is downside risk or upside potential when rates increase or decrease even if your returns of x are fairly stable and so they have to be included.

If anyone is interested I am looking at Sharpe and Sortino ratios.

Cheers.

You can all go back to sleep if you aren't, as is likely, interested.

Sharpe ratios are a silly metric anyway. "Risk-free" investments which show serious volatility are a pretty dumb idea.

Personally, if I were comparing two investments then I would use a geometric mean for Rf. Otherwise you run the risk of penalising equally volatile investments which are negatively correlated with the risk-free returns compared to those which are positively correlated.

[Kuciwalker]

I thought the point of a risk-free investment was that it wasn't volatile.

[KrazyHorse]

A volatile "risk-free" investment is one which has no (significant) possibility of negative return at any point.

[Kuciwalker]

That still seems silly, since it can still represent an opportunity cost.

[Solly]

Originally posted by Kuciwalker
That still seems silly, since it can still represent an opportunity cost.

That's why you want risk.

Gambling

[Kuciwalker]

Risk

[KrazyHorse]

Originally posted by Kuciwalker
That still seems silly, since it can still represent an opportunity cost.

I agree with you.

[Solly]

Originally posted by Kuciwalker
Risk

Being a gambler and risk-averse

[lord of the mark]

Originally posted by Kuciwalker
That still seems silly, since it can still represent an opportunity cost.

From what I remember of finance theory, a RF investment is usually considered to be one with no volatility. You cant evaluate the whether returns are "negative" or "positive" (given opportunity costs) until youve defined the opportunity cost in the market. The RF rates is the rate the market pays, in equilibrium, on a risk free (IE zero volatility investment)

I think we're not helping Dauphin at all.

[KrazyHorse]

No, technically the risk-free rate is the return which can be gained on financial instruments with 0 risk of default