The Concept of Risk and Return
June 15th 2007 12:26
Under the Investment Framework, investments are generally referred as assets with returns that are contingent upon future events unlike bank term investments with guaranteed returns (interest earnings) and generally risk-free.
Theoretically
Investments that are discussed here involve the trade off between current and future consumption. It is this trade off, the delay of current consumption by allocating resources into investment assets with an expectation of generating more resources for future consumption, that determine the rate of return and risk. The return is actually a mode for compensating the loss of current consumption opportunity. Hence the rate of return is also described as the rate of exchange of between future and current consumption.
Generally the rate of a return of an investment acts as an incentive for deferring current consumption. The other rationale for rate of return is the time value of money in which the degree of purchasing power in the future is affected by inflation. For instance, the value of money today is greater than the future as in the event of a future inflation rise, more money is needed to purchase an item than it was before.
The compensation does end with the trade off discussed earlier but its also affected by uncertainty as inflow of resources (future cash flow) are contingent upon future events that are favorable to the investment asset. But remember, future events that negatively affect the future cash flow could occur as well; therefore the issue of risk arises. And as such taking the risk in investing requires compensation as well, and the rate of return is adjusted accordingly to the degree of uncertainty.
Mathematically
There are two methods of obtaining realized returns; arithmetic and geometric, but in practice the arithmetic is usually used as it produce higher return values than the geometric method. Rate of return takes the form of percentage. The generic definition of return is the change in value of an investment asset over the holding period.
Arithmetic Return (Discrete/Simple Return)
Rt = (Pt – Pt-1) / P t-1
Geometric Return (Continuous Compounding)
This method of return calculation assumes that returns earned during the holding period are reinvested at the same rate of return whereas Arithmetic Return assumes returns earned during the period are immediately realized.
R = (1ADD Rt)^n – 1
--
R = return
t = time period
P = value or price of the investment
n = number of holding periods.
Expected Return
So far the discussion of return was in the context of realized return, another important element is expected return which is the future return of an investment asset subjected to future conditions or events. Realized return and expected return will be the same if future expectations are met. There could be a range of possible returns which are usually forecasted beforehand and each of the forecasted return will be given a probability weight obtained from analyzing data and prudent extrapolation.
E(r) = p1(r1) ADD p2(r2) ADD … ADD pn(rn)
Alternatively, expected return can be described as the expected average return of an investment.
Risk
The mathematical notion of investment risk is fronted by the statistical measure of variance, which is the deviation of each observation (returns) from the expected value (average return). Each point is then given a weight with heavier weights given to observations nearer to the average.
Var^2 = p1(r1 – E(r))^2 ADD p2(r2-E(r))^2 ADD … ADD pn(rn – E(r))^2
However, the standard practice is to use standard deviation rather than deviation which is the square root of the variance and therefore retains the same risk ranking.
--
P= probability (0 to 1)
R= return
N=holding period
Having discussed the basic concepts of risk and return which form the main elements of the investment framework, there are no clear cut prescribed methods of making a successful investment but these two elements provide an investor with the tools to evaluate the choice of alternatives. For instance, Asset A and Asset B have the same expected return of 10% but A has a lower standard deviation (risk) of 0.02 and B is 0.05, and in the assumption of a risk averse investor, Asset A will be the better choice of investment.
What was presented above is a mere basic outline of the framework which is to provide you with an idea how investment decisions are made using the elements of risk and return, at the theoretical level. The field of investment, academically and in practice, can be very complicated and could extend to other disciplines such as psychology and pure mathematics. But nonetheless, pocket the concept of risk and return as invesments are generally based on these two essential elements.
*Note: The Addition Sign, due to some various reason, could not be displayed. The Portal apologise for the inconvenience caused and will rectify the problem as soon as possible.
---
Related Posts:
Making the Move
Investment Framework: The Basics
---
Help to spread financial knowledge,
Make a Donation. Thank You.
Theoretically
Investments that are discussed here involve the trade off between current and future consumption. It is this trade off, the delay of current consumption by allocating resources into investment assets with an expectation of generating more resources for future consumption, that determine the rate of return and risk. The return is actually a mode for compensating the loss of current consumption opportunity. Hence the rate of return is also described as the rate of exchange of between future and current consumption.
Generally the rate of a return of an investment acts as an incentive for deferring current consumption. The other rationale for rate of return is the time value of money in which the degree of purchasing power in the future is affected by inflation. For instance, the value of money today is greater than the future as in the event of a future inflation rise, more money is needed to purchase an item than it was before.
The compensation does end with the trade off discussed earlier but its also affected by uncertainty as inflow of resources (future cash flow) are contingent upon future events that are favorable to the investment asset. But remember, future events that negatively affect the future cash flow could occur as well; therefore the issue of risk arises. And as such taking the risk in investing requires compensation as well, and the rate of return is adjusted accordingly to the degree of uncertainty.
Mathematically
There are two methods of obtaining realized returns; arithmetic and geometric, but in practice the arithmetic is usually used as it produce higher return values than the geometric method. Rate of return takes the form of percentage. The generic definition of return is the change in value of an investment asset over the holding period.
Arithmetic Return (Discrete/Simple Return)
Rt = (Pt – Pt-1) / P t-1
Geometric Return (Continuous Compounding)
This method of return calculation assumes that returns earned during the holding period are reinvested at the same rate of return whereas Arithmetic Return assumes returns earned during the period are immediately realized.
R = (1ADD Rt)^n – 1
--
R = return
t = time period
P = value or price of the investment
n = number of holding periods.
Expected Return
So far the discussion of return was in the context of realized return, another important element is expected return which is the future return of an investment asset subjected to future conditions or events. Realized return and expected return will be the same if future expectations are met. There could be a range of possible returns which are usually forecasted beforehand and each of the forecasted return will be given a probability weight obtained from analyzing data and prudent extrapolation.
E(r) = p1(r1) ADD p2(r2) ADD … ADD pn(rn)
Alternatively, expected return can be described as the expected average return of an investment.
Risk
The mathematical notion of investment risk is fronted by the statistical measure of variance, which is the deviation of each observation (returns) from the expected value (average return). Each point is then given a weight with heavier weights given to observations nearer to the average.
Var^2 = p1(r1 – E(r))^2 ADD p2(r2-E(r))^2 ADD … ADD pn(rn – E(r))^2
However, the standard practice is to use standard deviation rather than deviation which is the square root of the variance and therefore retains the same risk ranking.
--
P= probability (0 to 1)
R= return
N=holding period
Having discussed the basic concepts of risk and return which form the main elements of the investment framework, there are no clear cut prescribed methods of making a successful investment but these two elements provide an investor with the tools to evaluate the choice of alternatives. For instance, Asset A and Asset B have the same expected return of 10% but A has a lower standard deviation (risk) of 0.02 and B is 0.05, and in the assumption of a risk averse investor, Asset A will be the better choice of investment.
What was presented above is a mere basic outline of the framework which is to provide you with an idea how investment decisions are made using the elements of risk and return, at the theoretical level. The field of investment, academically and in practice, can be very complicated and could extend to other disciplines such as psychology and pure mathematics. But nonetheless, pocket the concept of risk and return as invesments are generally based on these two essential elements.
*Note: The Addition Sign, due to some various reason, could not be displayed. The Portal apologise for the inconvenience caused and will rectify the problem as soon as possible.
---
Related Posts:
Making the Move
Investment Framework: The Basics
---
Make a Donation. Thank You.
| 47 |
| Vote |
subscribe to this blog