Learning Material Sample

Investment principles, markets and environment

7. Measuring portfolio performance and investment management services

In this section, we introduce the concept of performance measurement and outline the limitations of past performan...

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...facet to them and will in their predictions, be reliant upon these factors staying the same in the future.


In this section we assess the various financial calculations used in evaluating portfolio performance. We start with an audiovisual presentation to help explain this topic.

Time Value of Money

A sum of money now is often likely to be worth more now than at a point in the future, because if invested, it can accumulate interest over the given time frame.

If interest is added to the sum of money i.e. reinvested, when the next interest payment is made, it will be based on a percentage of the original sum invested plus the already accumulated interest. This is known as compounding interest.


Ted deposits £15,000 into the Anytown Building Society which pays annual interest of 5% per annum compound. Interest is paid annually. He keeps the money in the account for 3 years. What will the funds be worth on withdrawal?


To carry out compound interest calculations, there are three alternative methods:

Use compound interest tables

Use mathematical formulae (manually)

Use a financial calculator (Hewlett Packard 10b recommended).

We will work through this section showing how calculations can be carried out using methods two and three, although you should be aware that compound interest tables exist and if these tables have been input onto for example, a Microsoft Excel spreadsheet, then you can use the relevant formulae and have the ability to vary data input relevant to each scenario.

Using mathematical formulae

The basic formula for the compound interest accumulation of a capital sum at an interest rate of “i” per year for a period of “n” is:


FV = PV (1 + i)

Where, FV is the future value and PV is the principal sum invested.

Using our example therefore,


FV = 15,000(1+ 0.05) = £17,364 (rounded down)

Using a financial calculator

The Hewlett Packard 10b calculator has the following functions that are used for compound interest calculations. Not all of the following keys will be needed with each calculation and we will guide you through which function keys to press for each type of mathematical sum we use:

Hewlett Packard 10b: Function Keys for Compound Interest Calculations


Number of annual compounding periods


Annual nominal rate of interest


Present value, or initial investment at the beginning of the first period


Amount of payments, which can be at the beginning or end of each period


Future value at the end of the last period

Shift + P/YR

Stores the number of compounding periods per year

Shift + BEG/END

Switches calculations between the beginning or the end of each period, i.e. whether payments in or out at the start or end of each period

Shift +xP/R

Stores the number of payments

As a general guide, problems can involve up to five variables and if four of these are known, it is possible to calculate the unknown value. If three variables are known, normally the fifth variable (not the result) should be input as zero.

In the above example the following keys would need to be input:




 1 Shift + P/YR


 Stores annual compounding period

 -15,000 PV


 Stores present value

 5 I/YR

 5.00 <...

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200 (1.0625)










The mathematical formula for calculating the accumulated sum derived from a series of regular payments is:


[(1 + i) - 1] / i

If the regular sum is invested annually in advance, the accumulated value can be found by adding a year’s interest to the above formula namely:


(1 + i) [(1 + i) - 1] / I .

Calculating the present value of a series of payments


The formula for calculating the present value of a series of payments is: (1 - v )/1.


It is the reciprocal of the future value calculation (1 + i).

Let’s consider an example using a financial calculator.


Jenny requires a capital sum of £50,000 in 8 years time. The effective annual rate of interest over the period is thought to be 8%. What monthly investment will be required?


12 Shift + P/YR = 12.00 (divides year into monthly payment periods)

50,000 FV = 50,000 (Stores future value)

8 Shift + xP/R = 96.00 (Stores number of payments (8 years is 96 months)

0 PV = 0.00 (Enter zero as there is no initial lump sum payment)

8 Shift + EFF% = 8.00 (Enters effective interest rate)

Shift + NOM% = 7.72 (Converts to nominal interest rate)

Shift + BEG/END = BEGIN (First monthly contribution is assumed to be immediate. If at the end of the first month, ensure that begin is not shown)

PMT = - 375.64 (Answer shows a negative sign because it represents a monthly outflow of cash

We can also apply similar calculations to find out how much can be withdrawn from an initial sum on a regular basis over a period of time if that sum is earning regular interest.


Natalie has invested £25,000 in Anywhere Bank plc paying a nominal rate of interest of 4% per annum. Interest is credited monthly and she wants to withdraw capital and interest so that in 5 years time, the account will reduce to zero. How much can be taken out at the start of each month?



12 Shift + P/YR = 12.00

25,000 PV = 25,000.00

0 FV = 0.00

4 I/YR = 4.00

5 Shift + xP/R = 60.00

PMT = - 458.88 (payment per month)

In this section we consider ways of calculating risk-adjusted returns.


When assessing the performance of an investment portfolio, it is important to take account of the risk that has been taken in achieving returns.

We previously considered the two ways in which risk is measured i.e. volatility measured by standard deviation of returns and systematic risk measured by beta.

We now take account of ways to measure risk-adjusted returns considering the following measures:

Sharpe ratio


We also consider the information ratio which can be used to assess the performance generated relative to a ben...

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...The risk taken relative to the benchmark is mostly measured by tracking error which is the standard deviation of relative returns.

The formula is:

Rp – Rb


tracking error


Rp = average annual portfolio return

Rb = average annual benchmark return


Average fund return is 14%, benchmark return is 10% and tracking error is 6%.

Information ratio is (14-10) / 6 = 0.666

The higher the positive information ratio the better the risk-adjusted return based on performance relative to the benchmark. An information ratio above 0.5 would usually be considered very good.


In this section we consider the different available indices which allow us to benchmark performance against the relevant market.

Stock market indices bring together the movements of company share prices and show which way the market moves over time.

They give the ability to measure performance of a portfolio of shares over different periods.

The index provides a number used to compare the value of companies at different points in time.

They can be used for a number of reasons:

Comparison of performance of a particular share with its sector of the market as a whole

To evaluate market movements with the intention of predicting trends that may continue in the future

Compare the performance of a fund manager with the performance of the market as a whole. Many active fund managers aim to beat the market. Passive fund management aims to track the market.

Variety of Indices

The majority of indices around the world relate to equities but there are indices that reflect most types of investment.

Portfolio managers will choose the most appropriate index from which to comp...

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...ks the NASDAQ market and is often used as a proxy for the performance of US technology stocks.


The most widely used index is the Nikkei 225. It is not strictly an index but is based on the average price of 225 stocks which are not weighted by market capitalisation.


The DAX 30 consists of the largest 30 quoted German companies calculated in real time. The index includes reinvested income.

Hong Kong

The Hang Seng Index is designed to serve as an indicator of the broad movements of the Hong Kong stockmarket. It is composed of a representative sample of Hong Kong stocks.


The CAC General Index records the opening prices on the Paris cash market while the CAC 40 is a real time index of the largest stocks.


The FTSE operates the FTSE All-World Index which comprises around 3,000 stocks from 47 countries. The newer FTSE Global All-Cap Index covers nearly 8,000 stocks. In addition there are a range of indices covering Europe, Asia Pacific and world indices that exclude certain countries such as the USA, Japan, Eurobloc and UK etc.


In this section we attempt to measure the performance of a portfolio given certain key formulae and principles to follow.

Performance Measurement

Performance measurement simply means the measurement of the performance of a portfolio over a given time frame. It does not compare the performance against other investments or perhaps, a benchmark index. This is dealt with later.

There are two main ways to calculate the return from a portfolio. These are:

Money weighted return (MWR)

Time weighted return (TWR)

Money weighted return measures the return of capital invested over a particular period, whereas time weighted return allows comparisons to be made of the performance of one fund manager to another.

Money Weighted Return

Portfolio returns are expressed as being equal to the total of:

The difference in value of the portfolio at the end of the period and the value of the portfolio at the start of the period plus any income or capital distributions made from the portfolio during that period.

The rate of return expresses the money return in terms of the amount of the value of the portfolio at the beginning of the period.

                                      (V1 – V0 + I)

The formula for this is: R =  -------------



R is the rate of return

V0 is the value of the portfolio at the start of the period

V1 is the value of the portfolio at the end of the period

I is the income or capital distribution during the perio


A portfolio is valued at £30,000 at the start of a period and £36,000 at the end of the period. There was also income of £560 paid out from the portfolio.

MWR = (36,000 – 30,000 + 560)/30,000

= 0.21866 or 21.867%

If new money is invested or funds withdrawn during the year, then the formula can be amended to allow for the differences in the timing of these.

The equation is:

R = (V1 – V0 – C)/[V0 + (C x N/12)]


C is the new money introduced during the year

N is the number of months remaining in the year


A portfolio was worth £14,500 at the start of the year, and £18,000 at the end of the year. In addition, the following transactions were made:

£2,000 invested at the end of February

£1,500 withdrawn at the end of November

The money weighted return is:

(18,000 – 14,500 – 500)/[14,500 + (2,000 x 10/12) – (1,500 x 1/12)]

= 3,000/(14,500 + 1,667 – 125)

= 0.187

Or 18.7%

Money weighted return is strongly influenced by the timing of cash flows that are outside the control of the portfolio manager. They therefore don’t identify whether performance is due to the fund manager or the cash flows.

Time Weighted Return

Time weighted return tries to address the pitfall of money weighted returns by breaking down returns into sub periods that show the return for each time capital is added or withdrawn. Time weighting for the overall period is calculated by compounding the returns for each sub period.

The formula for time weighted return is:

1 + R = V1/V0 x V2/(V1 + C)

Where R is the return in the overall period


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...vestment objectives

It is relatively difficult to find much information about the performance of portfolio management services when say compared to collective investment schemes

Smaller funds can be easier to manage than larger ones

Investors should seek consistency in performance when taking account of such factors as volatility

Most portfolios resemble one another closely and differences in fund performance between managers tend to arise from relatively small differences in the portfolios. Some will operate differently from the norm and investors should be aware of the risks involved in any variation in investment strategy.

Comparing Collective Investments

Performance statistics for collective investment schemes include the following:

- Tables in magazines, newspapers and the internet

- These will include league tables showing top and bottom performers

- Tables are often divided into sections in accordance with the type of collective scheme and fund category.

Information about these schemes will include:

- Values of £1,000 invested over certain periods e.g. 1 year, 5 years,10 years

- Rankings within sector

- Some tables will show year by year performance which avoids cumulative distortion

- Volatility measured by standard deviation

- Charges

- Fund size

- Launch date

- Fund yields

- Whether open to new business

- Other relevant information

Computer systems

Designed mainly for PCs and provide the same type of information as data base systems. Main differences are:

- More information in graphical form allowing for daily or weekly fluctuations to be shown

- Information is easy to manipulate and compare in graphical form over different time periods.

Median, Quartile and Average

Participating funds of portfolios are ranked in accordance with performance for total return and in relation to individual sectors. It is usual to assign portfolios to a quartile ranking. All returns are set out in descending order:

- The median return is exactly halfway down the list

- The upper quartile is the return one-quarter of the way from the top

- The lower quartile is the return one quarter of the way from the bottom


A particular sector has 200 funds in a sample. Therefore each quartile consists of 50 funds.

Fund managers often express the desire to be consistent to be top quartile performers – i.e. among the highest 25% of funds.

The median in this example is the return achieved between the 100th and 101st portfolio participating in the sample.

The quartile values give an indication of the spread of the results around the median.

The median is often used as the basic statistic as using mean averages could give a distorted view bearing in mind the extremes of results created by top and bottom performers.

Analysing other information

Although figures will create a starting point, other information can be obtained about the managers and management of a portfolio or fund:

- Who is the management team of the fund?

- Who has been responsible for past performance?

- What is the personal track record of the fund manager?

- What is the investment strategy e.g. top down asset allocation or bottom up stock selection?

- How strong is the performance monitoring of the investment management company?

- What are the fund’s objectives?

Finally, when choosing an investment manager, it is important to consider some further factors to take into account such as:

Relevant experience

Performance over the past

Structure and style of investment

Quality of staff and stability

Administration ability



In this section we discuss the criteria that can be considered when choosing an investment manager.

Relevant experience

The experience of the investment manager should coincide with the investments being handled and the client’s overall objectives.


The general intention should be to target investment managers that can...

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...s than would otherwise be the case with an unsettled team.


Good quality and fast administration services are more important than ever in such a competitive market.

Charges and costs

Costs have become a greater issue in these lower inflation times as a change to them will have a more profound effect on real returns.


In this section we briefly discuss the effect of past performance on choosing an investment manager.

As already mentioned, there is li...

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... objectives than those being currently adhered to

Measuring returns alone does not account for the risk that has been taken.


In this section we summarise the role of investment portfolio managers and identify the differences between acting on an advisory or a discretionary basis.

Summary of the role of portfolio managers

The role and responsibility of the portfolio manager is to:

Assist clients to determine and prioritise their needs

Determine an appropriate in...

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...estment manager.

The main items of reporting will often be:

Purchases and sales

Summary portfolio valuation and statements showing income, interest received, dividends and cash outflows

General market commentary and calculated investment returns compared with the agreed benchmarks

Recommended changes to the investment strategy.


In this section we discuss the options that can be covered within a managed investment portfolio and consider the main benefits and pitfalls of each.

Direct investment

Direct investment is usually only suitable where portfolios are large enough in order to be able to accommodate charges and provide sufficient diversification among investments.


Many clients are interested in having direct holdings in particular companies whose fortunes they enjoy following

Direct investment is likely to interest investors prepared to accept risk to a certain degree

Low costs on switching investment managers due to the transferability of stocks without the need to encash them

The portfolio can be tailored to accommodate the investor’s requirements

It is easier to exclude holdings in specific stocks

Greater transparency of costs

Exemptions and reliefs can be used to offset capital gains made that are subject to CGT

Larger portfolios can enjoy an economy of scale and lower expense ratios than can be achieved via collective investments.


Potentially higher volatility of performance because fewer investment s are likely to be held compared to a collective investment

Costs are higher for smaller portfolios

Usually need greater involvement by an investment manager

Results may be more volatile as they depend on individual managers and the performance of one or two stocks can provide a disproportionate effect on returns

It may be necessary to switch investments more within a large portfolio thus potentially incurring gains subject to CGT (after exemptions and allowances)

Potentially more administrative costs than with collective investments

VAT will be charged on management fees which are not tax relieved in any way.

Collective Investment

Collective investment holds several attractions not least the ability to pool relatively small resources with others...

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...ught and sold must be the same and the price should be published daily.

ISA providers

There is a choice between many individual ISA managers. Some managers only offer cash ISAs or only Stocks and Shares ISAs. Others offer both components.

Existing ISAs, PEPs

If savers have invested previously in mini cash ISAs, TESSA-only ISAs (TOISAs) or the cash component of a maxi ISA, these automatically from the start of the new tax year on 6th April 2008 became cash ISAs.

If savers have invested previously in mini stocks and shares ISAs and the stocks and shares component of a maxi ISA, these will automatically become stocks and shares ISAs. All Personal Equity Plans (PEPs) will automatically become stocks and shares ISAs.

ISA Transfers

It is possible to transfer some or all of an investor’s funds saved in a previous tax year into another ISA without affecting ISA subscription limits for the tax year.

Savers may also transfer money saved in the current tax year in an ISA to another ISA provider. If this course of action is taken, the whole amount saved in the current tax year must be transferred.

It is possible to transfer the funds held within a cash ISA to a stocks and shares ISA but not the other way around.

ISAs cannot be transferred to another person.

Tax advantages of an ISA

An ISA wrapped investment will benefit from tax advantaged growth within its own fund. There will be no tax to pay on any income or capital gains arising within the fund (although dividend tax credits cannot be reclaimed) and investment proceeds to the saver will be free of any income tax or capital gains tax.


There is generally no lock-in period for ISAs and withdrawals are possible at any time, without loss of the tax advantages. This may not be the case if investors choose to save in an ISA that, in return for offering extra benefits such as a guarantee, may offer you less flexibility.


In this final section we discuss charges that can apply to both direct investment portfolios and collective investment schemes.

Direct investment

Charges levied by investment managers and stockbrokers could include:

Stamp duty at 0.5% on shares

Private client stockbroker fees which vary depending upon the value of secu...

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... all fees for buying and holding underlying investments and for administration within the wrap account. These fees can be between 0.5% to 2% of the portfolio’s value per year depending on size. Some wrap accounts may charge a small percentage of the portfolio but it is then up to the investor to incur dealing costs etc.


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