Inputs: Expected Return III

Inputs: Expected Return III
Hi,
I don’t understand anything about this computing.
In the sample we compute with the following formula:

Our sample dataset is:

Company Weight Return
Company 1 .1 3%
Company 1 .3 7%
Company 1 .25 12%
Company 1 .35 2%

The sample follow the above formula and compute the compute the expected return:

The expected return is equal to 6.1%.
This value falls in the middle of the expected return range of the four companies.
So if I understand well our expected return always must be between the smallest and highest return of the dataset.
The smallest is: 2%
The highest is: 12 %


Exercise:
  1. Calculate the expected return of a portfolio with the following asset weights and expected returns:

    Company Weigh Return
    Nike .8 1.4%
    Under Armour .16 .8%
    Skechers .04 7.0%

Followed the above sample my solution is:

expected_return = 0.8 * 1.4 + 0.16 * 0.8 + 0.04 * 7
"The expected return is equal to 1.53%"

This result is between the minimum (0.8%) and the maximum (7%)
My result fails on the test.

I viewed the solutions witch is:

expected_return = .8 * .014 + .16 * .008 + .04 * .07
expected_return  = 0.015280000000000002

So the sample compute with percentage but the exam solution compute with the floating number…
I cannot understand…

Hi,

If you want to generalize the expected range with a bound, you have to first multiply the w*R. (For example, if the return was 12% and the weight is 0.001, the expected return for this pair would be 0.00012, whereas if the return is 1% and the weight is 100, the eR would be 1, which is larger). In this given example, 2% * .35 is 0.07, whereas 3% * .1 is .003. So 2% doesn’t represent the lowest expected return (even though it is the lowest return).

When doing arithmetic with percentages it’s accurate to translate them to floating numbers… unless you write a special function to parse it, which is usually unnecessary. What is easier to do is to parse the final answer into a percentage by multiplying by 100 and adding a char “%” at the end (or something along those lines.

The practice of using floating numbers in these cases may be by convention but it’s useful in that it is explicit (nobody looking will confuse the number to be anything other than what it is). It may be that other conventions shortcut by using 1.4 instead of .014 but when in doubt, .014 is always the safer option.