Measuring Return

Question 1

What is total return or holding period return?

How do you calculate it?

Answer 1

This is the total return you get from the change in value of the asset (capital growth) and the income you receive.

To calculate add the income (D) and the capital gain (V1-V0) together (or deduct capital loss) and divide by the original price (V0).

Question 2

What is relative return?

Answer 2

This is the return achieved relative to a given benchmark.

So if your portfolio returned 10% and the benchmark index rose by 8%, you achieved a relative return of +2%.

Question 3

What is the difference between money-weighted and time-weighted rate of return?

Which one can you use to compare fund managers performance?

Answer 3

Money-weighted is affected by when you put money in or took it out, so it is your personal performance. This could be higher than the performance of the portfolio itself if you were lucky enough to put more money in at a low point.

Time-weighted ignores when you put money in or took it out, it just considers the performance of the portfolio over time. This is the one you use to compare fund managers with each other.

Question 4

Calculating return

How do you calculate return in the event that you borrowed some money to fund the investment.

For example, you have £50k to invest and you borrow a further £20k and invest it all in a fund. The fund returns 10% performance over the year. You pay 5% interest on the borrowing. What is your return?

Answer 4

You need to calculate how much money you’re left with at the end.

£70k was invested with a 10% return so that leaves £77k at the end of the year.

But you have to pay back the £20k and £1k interest (=5%*£20k) so you are left with £56k.

So your return is 56k/50k - 1 = 12%.

Or do (56k - 50k) / 50k = 12% if that is easier for you.

Question 5

Calculating Return

How do you calculate the time weighted return when there is money being taken out or put in during the year?

For example, you start by investing £100k, which grows to £110k after six months and pays a £5k dividend on top.

You take out £20k (the £5k dividend and £15k of the investment) and the remaining investment ends the year at £105k.

What is the time weighted return?

Answer 5

What you need to find out is the return in each of the two periods and multiply them together (with a +1 like compound interest).

The first six months return (£110k + £5k - £100k) / £100k = 15%.

The next six months you invest £95k (after taking out the £5k dividend and £15k of the £110k investment) and it rises to £105k.

So your return in the second half of the year is (£105k - £95k) / £95k = 10.5%.

So the time weighted return over the year is (1 + 15%)*(1 + 10.5%) - 1 = 27.1%

Question 6

What 4 factors does performance evaluation assess?

Answer 6

• Asset Allocation (stocks vs bonds vs property)
• Stock selection (specific stock choices)
• Market timing (impact of when you invest, when you take money out)
• Risk (the amount of risk you take to achieve the return)

Question 7

Risk Adjusted Returns

What does this mean?

What is the purpose?

Answer 7

Risk adjusted return is a performance measure, a calculated number that tells you how well the investment has performed.

More specifically it is a return figure which takes into account how much risk you took to achieve that return.

So if you achieved a high return (say 15%) but took a massive amount of risk to get there, these measure will show that you didn’t do so great.

Question 8

Risk Adjusted Returns

What are the 3 risk adjusted return measures?

What risk measure do they each take into account?

Answer 8

• Sharpe ratio (takes into account standard deviation)
• Information ratio (takes into account tracking error)
• Alpha (takes into account beta)

Question 9

Risk Adjusted Returns

What is the Sharpe Ratio calcualtion?

Answer 9

Sharpe Ratio

(Return on investment - Risk Free Return) / Standard Deviation

Question 10

Risk Adjusted Returns

What is the Information Ratio calculation?

Answer 10

Information Ratio

(Portfolio Return - Benchmark Return) / tracking error

Question 11

Risk Adjusted Return

How do you calculate alpha?

Answer 11

Alpha

First calcualte the expected return as per the CAPM equation:

Expected return = Risk free rate + Beta * (market rate - risk free rate)

Then Alpha = Actual investment return - expected return

Question 12

Risk Adjusted Return

Do you want this to be high or low?

Answer 12

Just like return itself, you want it to be high.

Question 13

Risk Adjusted Return

How is sharpe ratio affected if standard deviation increases?

Answer 13

If the level of risk (i.e. standard deviation for sharpe ratio) increases, that means your risk adjusted return will decrease.

It means you’ve taken more risk to achieve the same return, so you haven’t done as good a job.