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Q: Can any ratio be written as a unit rate?

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a non-stop rate * * * * * No it is not. A non-stop rate can be faster and slower and faster and faster still etc. That is NOT a constant rate, A constant rate means the same amount for any unit of time in the whole time interval. The rate must not change at all from start to finish.

Any ratio of the form p : q where p and q are integers whose absolute values are greater than 1.

The ratio of the circumference of a circle to its diameter is Pi. (3.14159)

The ratio of the circumference of a circle to its diameter is Pi. (3.14159)

I've written before about the Sharpe Ratio, a measure of risk-adjusted returns for an asset or portfolio. The Sharpe ratio functions by dividing the difference between the returns of that asset or portfolio and the risk-free rate of return by the standard deviation of the returns from their mean. So it gives you an idea of the level of risk assumed to earn each marginal unit of return. The problem with using the Sharpe Ratio is that it assumes that all deviations from the mean are risky, and therefore bad. But often those deviations are upward movements. Why should an investment strategy by graded so sharply by the Sharpe Ratio for good performance? In the real world, investors don't usually mind upside deviations from the mean. Why would they? These were the questions on the mind of Frank Sortino when he developed what has been dubbed the Sortino Ratio. The ratio that bears his name is a modification of the Sharpe Ratio that only takes into account negative deviations and counts them as risk. To me, it always made a lot more sense not to include upside volatility from the equation because I rather like to see some upside volatility in my portfolios. With the Sortino Ratio only downside volatility is used as the denominator in the equation. So the way you calculate it is to divide the difference between the expected rate of return and the risk-free rate by the standard deviation of negative asset returns. (It can be a bit tricky the first time you try to do it. The positive deviations are set to values of zero during the standard deviation calculation in order to calculate downside deviation.) By using the Sortino Ratio instead of the Sharpe Ratio you’re not penalizing the investment manager or strategy for any upside volatility in the portfolio. And doesn’t that make a whole lot more sense?

Related questions

Pi is a natural constant of the ratio circumference divided by diameter. That ratio cannot have any unit.

The index of refraction is a unitless ratio. It has no units, it is a pure number.

A unitary rate must specifically have a denominator of one. Unitary rates are used in mathematical operations and conversions. Any other ratio can have any number as the denominator.

Any type of measurement is a unit rate. The speed limit is a measurement of time and distance.

A proportion is the same as a ratio, but it must be focused on one unit per something. Ratios can be any comparison

-- Any number that can be written as the ratio of two whole numbers is a rational number.-- Any whole number can be written as the ratio of that number to ' 1 ', so it's rational.

Compounds are represented by a formula unit to show the simplest ratio of atoms or ions. This unit repeats throughout any amount of the compound.

Any and every rational number.

They are rational numbers.

It is a rational number.

The same way you round any number to the nearest hundredth.

Any measure must always be written in units unless it is a pure ratio.

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