Chapter 13 - Portfolio construction (15 questions (included with chapter 12))

Question 1

Now that we have all the client information, their objectives and risk profile, how do we go about constructing portfolios for them?

In this chapter, we’ll start with the measurements of risk and return and see how these are used to build a portfolio for a customer. We’ll also explore the principles of diversification and correlation, and the role they play in reducing risk.

We’ll look at Modern Portfolio Theory (MPT) and all its constituent parts, and the implications of the Efficient Market Hypothesis (EMH) and behavioural finance.

Now that we have all the client information, their objectives and risk profile, how do we go about constructing portfolios for them?

In this chapter, we’ll start with the measurements of risk and return and see how these are used to build a portfolio for a customer. We’ll also explore the principles of diversification and correlation, and the role they play in reducing risk.

We’ll look at Modern Portfolio Theory (MPT) and all its constituent parts, and the implications of the Efficient Market Hypothesis (EMH) and behavioural finance.

Question 2

13.1.1: Modern portfolio theory (MPT)

Answer 2

Modern Portfolio Theory is all about the way portfolios of investments can be structured to maximise returns and minimise risks.

investors are risk-averse and would choose a less-risky investment if they were given the choice of two that offered the same return.

Question 3

What are mean, median & mode used for?

Answer 3

Different ways to calculate averages

Mode = most
Median = middle
Mean = Add all up and divide by how many there are

The mean is the one that is used within investment analysis to understand the average return that has been achieved.

Question 4

So, what is ‘normal distribution’?

It means that most of the examples in a set of data are close to the ‘average’, whilst relatively few examples tend to be at one extreme or the other.

This can apply to all kinds of data, such as people’s heights, blood pressure results, the marks scored on J12 or, for our purposes, the returns on an investment.

The mathematical measure of how tightly the data is gathered around the ‘mean’ is known as standard deviation.

When the results are pretty tightly bunched together, and the bell-shaped curve is steep, the standard deviation is small.

Most results are pretty near the average.

When the results are spread apart, and the bell curve is relatively flat, that tells you that you have a relatively large standard deviation.

So, the returns have tended to vary quite a lot.

Question 5

Standard deviation in relation investing

Answer 5

SD measures how widely the actual return from an investment varies arounds its average or median

The greater, the more it varies, which means higher volatility

Question 6

In ‘normally distributed’ data…
o 68% of outcomes will be within 1 standard deviation of the mean

    o    95% of outcomes will be within 2 standard deviations of the mean

    o    99.7%+ of outcomes will be within 3 standard deviation of the mean

AND

Standard deviation measures how widely the actual return from an investment varies arounds its average or median

The greater, the more it varies, which means higher volatility

Answer 6

The BTS fund has a mean of 9% and a standard deviation of 2%.

1 standard deviation it could fluctuate between 7-11% = 68% of the time we would expect this return

2 standard deviation it could fluctuate between 5-13% = 95% of the time we would expect this return

3 standard deviation it could fluctuate between 3-15% = 99.7% of the time we would expect this return

Question 7

IMPORTANT = Standard deviation is an acceptable measure of risk ONLY if the returns are ‘distributed normally’.

Answer 7

The issue here is that returns may not always follow a normal distribution. The peak may be skewed to the left (positive skew) or the right (negative skew), which can means that risk can be over or under estimated. The technical term for this skew is kurtosis

Question 8

13.1.1b: Systematic (market risk) and non-systematic risk

What is Beta?

Answer 8

It tells us how much a security or portfolio will move in line with the market.

The market has a beta of 1 as it is the benchmark against which a security’s beta is measured.

An asset’s beta will show the extent to which that asset moves (up or down) in line with changes in the market in which that security fits.

Question 9

Systematic (market risk) = unavoidable

Non-systematic risk = Can be reduced through diversification

Question 10

The efficient frontier

Answer 10

It explains the relationship between the return that can be expected from a portfolio and the portfolio’s risk.

Shows the best return that can be expected for any given level of risk. An investor will want their investment to be as close to the efficient frontier as possible as it means that their portfolio has performed the best it can for the level of risk taken

This is used alongside the modern portfolio theory

Question 11

The efficient frontier is not without its critics and limitations:

It assumes that investment returns follow a ‘normal distribution’ pattern, and that standard deviation is the correct measure of risk.
For some investors, ‘attitude to risk’ may not be their only or key consideration. For example, they may have ethical preferences that mean some portfolios are unacceptable to them.
It works on historic data and, as we know, past performance is no guide to future performance.
The model takes no account of charges within the investments.
It is difficult to get sufficient data to plot the graph.

Question 12

Some securities are more sensitive to systematic risk.

Question 13

What is the 13.1.2: Capital Asset Pricing Model (CAPM)

Answer 13

This is an extension of MPT

CAPM states that ‘in order to consider a risky asset, an investor would want a return that equals the risk-free return plus, as a form of compensation, an additional return that takes account of the risks taken’.

To understand CAPM, we need to consider that all investments have a notional element of risk-free return (typically cash) and a notional element of risk-based returns (other asset classes).

CAPM measures the riskiness of a security by comparing it to the market. It uses beta (β) as part of its measure.

Question 14

REMEMBER: Markets have a Beta of 1. The investment that you compare the market to has a Beta that varies (the market is the benchmark)

Answer 14

LESS volatile than the market = Beta of less than 1

MORE volatile than the market = Beta of more than 1

If a security has a beta of 1, it has, historically, matched the market’s volatility exactly.

Question 15

The higher the beta of a security; the higher the risk and the higher the return investors should expect, so that they are rewarded for taking the added risk. This is according to CAPM

Answer 15

Beta of 0.2 = 80% less volatile than the market = If market falls by
10%, the shares are likely to fall by 2% and vice versa

This is based on part data and is not a guarantee

Question 16

13.1.2b: CAPM formula

Question 17

ASSET ALLOCATION is responsible for almost 90% of the variability between performance of differing portfolios

Question 18

Difference between strategic and tactical asset allocation

Answer 18

A fund may choose their asset allocation percentages and stick to those percentages; rebalancing the portfolio regularly to ensure that the percentages are maintained. This is known as strategic asset allocation.

Other funds may allocate the asset classes within a range, to give the fund manager a bit of scope to take advantage of market opportunities by being overweight in one asset class and underweight in others at any one time. This is known as tactical asset allocation.

Question 19

Look at 13.7. It is a rebalancing question

Question 20

What are strategic ranges?

Answer 20

Tactical asset allocation is a more hands-on approach than strategic asset allocation.

It involves the short-term variation of the asset allocation of the fund (within pre-defined ranges) in order to take advantage of market changes or fluctuations.

Investment managers seek to counterbalance the defensive tendencies of asset allocation methodology by applying tactical asset allocation.

More often than not, tactical asset allocation models are present in discretionary managed portfolios rather than advisory ones.

A fund manager is ‘applying their skills’ far more in a tactical model than in a strategic one.

With tactical asset allocation, you start with a base allocation, such as the 60% shares, 30% bonds, 10% cash allocation we used in the strategic example, but have a range of (for example) plus or minus ten or twenty percent within each asset allocation.

These are known as strategic ranges.

The fund manager must ensure that she stays within the bands, so if we assume 20% bands, in our example shares could go anywhere between 40% and 80%, bonds anywhere between 10% and 50%, and cash zero to 30%.

So, rather than following a static allocation and rebalancing on a periodic basis, the manager can choose to overweight or underweight asset classes, (basically being at the top or bottom of the bands at any one point) based on an assessment of the value of the asset.

If the fund manager was feeling bullish on equities and bearish on bonds, then they could easily switch the asset allocation from 60,30,10 to 70,20,10.

Tactical asset allocations put far more onus on the adviser or fund manager to monitor the market and vary the portfolio to suit market conditions.

Question 21

What are closet trackers?

Answer 21

Actively managed funds that basically just tracked an index due to the fund managers selection. Regulators forced them to pay compensation to the investors who had paid higher charges for the active management

Question 22

13.5.1b: Active bond strategies

There are 3 types of active bond strategy:

Riding the yield curve
Anomaly switches
Policy switches

Question 23

13.5.2b: Passive bond strategies

Fund managers don’t just include bonds in their client’s portfolio to benefit from a rise in their price (although of course that is an added bonus!). Sometimes they are using them to help meet their client’s investment objectives to match a future liability.

There are three bond strategies that you should be aware of.

Cash flow matching o    As the name suggests, this is where bonds are purchased where either the redemption proceeds or the coupons match future liabilities. 

o This could simply be achieved by buying a bond whose maturity matches that of a future liability.

o A bullet strategy (single bond) or a ladder approach could be taken. With the ladder strategy, a series of bonds with different maturities are purchased and the proceeds used for the future liabilities. Say for example you had school fee payments to make for the next 5 years; you could buy a 1-year, 2-year, 3-year, 4-year and 5-year bond using the proceeds when each bond redeems to pay that year’s fees.

Duration matching or immunisation
o This is another term for hedging interest rate risk.

o It ensures that the duration of the portfolio’s assets matches the duration of the future liabilities to ensure that the value of a portfolio is protected against changes in interest rates.

Barbell strategy
o This is another passive strategy, whereby the duration of a liability is matched using bonds with a maturity either side of the maturity of the liability.

o For example, a 7-year liability can be matched by holding 5-year and 10-year bonds.

o This strategy will require a greater amount of rebalancing than a bullet strategy.

Horizon or combination matching
o This isn’t a separate strategy. It is more a combination of cash flow matching and immunisation.

o The portfolio cash flow matches short-term liabilities and then immunises the remaining liabilities.

Question 24

What are core-satellite strategies?

Answer 24

As there are different views on which is best, active or passive, there are funds that incorporate both strategies!

With core-satellite strategies, you could have a core, for example 80% of the fund, indexed to minimise the risk of underperformance.

Then the remainder could be invested in a number of specialist actively managed funds, or individual securities, known as satellites.

Many different management styles can be combined in this way, such as value, or momentum investing, along indexation or buy and hold cores.

Question 25

13.6: Evaluating Portfolio Risk and Return
Let’s look at two funds:

Fund A has returned 10% over the last year and has a standard deviation of 7%
Fund B has returned 8% over the same period with a standard deviation of 4%

Which fund is better?

From a pure performance point of view Fund A looks better but they have taken more risk as measured by the standard deviation.

It’s therefore useful for investors to look at risk-adjusted returns.

They attempt to give a measure of return per unit of risk and separate out how much of the return came from the risk taken and how much of the return was due to the expertise of the fund manager.

Alpha, Sharpe ratio & information ratio are used for this

Tell me about each

Answer 25

13.6.1: Alpha

Calculate expected return using CAPM formula

Expected return = (Risky x Beta) + risk free
Risky = market return - risk free

then,

Alpha = actual return - expected return

Question 26

Calculating Alpha:

Alpha or Jensen’s alpha or Jensen measure is the difference between the actual return on a security and the expected return that you would get using CAPM. The CAPM return is the return you would expect given the stock’s beta, so anything over and above that (the alpha) must be down to the stock-picking skills of the manager.

A positive alpha would suggest that the fund manager has done a good job, a negative alpha, a not so good job. The higher the alpha, the better the job the fund manager has done. It can be expressed as:

It is a useful measure for active funds (it should be close to zero for passive funds).

Answer 26

Calculate expected return using CAPM formula

Expected return = (Risky x Beta) + risk free
Risky = market return - risk free

then,

Alpha = actual return - expected return

Ie, ‘What you achieved’ MINUS ‘what you’d have expected based on CAPM’.

Question 26

13.6.2: Sharpe ratio

Sharpe ratio tell us how much excess return is achieved per unit of risk. It enables us to understand whether the returns have been generated by excessive risk-taking or due to the skill of the fund manager.

A higher Sharpe ratio suggests a skilful fund manager, a lower Sharpe ratio suggests greater risk has been taken to achieve returns. The Sharpe ratio can be positive or negative.

Calculating Sharpe Ratio:

Answer 26

(Actual return - risk free return) / standard deviation

(The higher the standard deviation, the lower the Sharpe ratio.)

Question 27

13.6.3: Information ratio

The information ratio again gauges the success of the fund manager.

It expresses the excess return of a benchmark against how much excess return was expected i.e.

The higher the information ratio, the better the skill of the fund manager.

Answer 27

(Portfolio return - benchmark return) / tracking error

Question 28

In this chapter, we have looked at the following areas:

Risk and Return

MPT suggests that portfolios can be constructed that maximise returns, and minimise risk, by carefully choosing different investments.
Diversification can be used to reduce risk.
Average returns can be based on the mode, median and mean values.
The mean is used for investment analysis as the average return that has been achieved.
The most commonly used measure of risk is standard deviation. The higher the standard deviation, the higher the volatility and therefore the higher the risk.
Standard deviation uses the variance from the mean to help predict likely future performance.
In normally distributed data.
o 68% of outcomes will be within 1 standard deviation of the mean.

o 95% of outcomes will be within 2 standard deviations of the mean.

o 99%+ of outcomes will be within 3 standard deviations of the mean

There are two component risks: Systematic or market risk, which you cannot diversify against; non-systematic or investment risk, which can be removed with careful fund selection.
The efficient frontier explains the relationship between the return that can be expected from a portfolio and the portfolio’s risk (as measured by standard deviation).
The efficient frontier plots funds with the ultimate portfolio sitting on the efficient frontier line.
Capital Asset Pricing Model (CAPM)

CAPM is a model that provides the theoretical expected return for a security as a combination of the return on a risk-free asset and the added return on risky assets.
It uses beta as its measure of risk.
Beta measures the risk of an asset compared to the market portfolio.
The market always has a beta of 1.
A beta of >1 shows that an asset is riskier than the market, a beta that is < 1 is less risky than the market.
It is based on assumptions, some of which hold more sway than others.
Multi-factor models

These add additional factors to the CAPM calculation as part of their assumptions.
Efficient Market Hypothesis

EMH argues that active fund management is more about luck than judgement, in many cases.
It states that information about companies is freely available and, as such, the prices of securities always reflects the companies’ true worth.
There are three forms: Weak, Semi-strong and Strong.
If EMH is correct, investors would be best served by passively managed tracker funds, as opposed to expensive fund managed portfolios.
Behavioural finance

Contrary to technical analysis, believers in behavioural finance put more emphasis on psychological factors.
Investors are more upset by losses than they are happy with gains.
Some investors find it difficult to decide to sell at a loss when, actually, they would be better off cutting those losses.
Investors also tend to try to protect gains but are far more adventurous when trying to make up losses.
Portfolio risk

The main risks in a portfolio include: capital, inflation, interest rate, currency, investment performance, counterparty, and liquidity risks.
Gearing or leverage is inherent in investment trusts. It magnifies gains but also magnifies losses.
Risk management

Low risk portfolios can be constructed either through buying low-risk assets or through diversification.
The effectiveness of diversification depends on how the assets correlate with each other.
Combining different asset types, in different sectors, over different geography, can all help the effective diversification of a portfolio.
Diversification is best achieved by combining assets that have low or negative correlation between them.
Correlation can be positive, negative or no correlation.
Risk can also be reduced by hedging or immunisation.
Asset allocation

Asset allocation is about selecting a mix of assets that match a client’s investment objectives and risk profile.
Advisers will create model portfolios that align with different risk categories.
A cautious investor with a low attitude to risk will have a higher proportion of fixed income and a lower proportion of equities than a more adventurous investor.
The mix of assets is known as strategic asset allocation.
Portfolio managers may use the benchmark as the basis for the asset allocation.
Strategic asset allocation is about meeting long-term goals.
Portfolios will need to be regularly rebalanced to maintain the asset allocations.
Tactical asset allocation defines bands within each asset class that the manager must keep within.
Tactical asset allocation allows for flexibility; the fund manager can take advantage of market opportunities.
Investment strategies

Investment management styles can be passive or active.
Active styles seek to actively outperform a predetermined benchmark whilst passive styles will track a benchmark.
Active equity strategies include top-down and bottom-up.
Active bond strategies include riding the yield curve, anomaly switches and policy switches.
Anomaly switches include substitution switches and pure yield pick-up switches.
Policy switches include benefitting from a change in interest rates, change in the yield curve, change in credit ratings or a change in sector relationships.
Passive equity strategies will track an index but will have a tracking error.
Passive bond strategies include cash-flow matching, immunisation or duration matching, and combination or horizon matching.
Core satellite strategies involve a mix of passive and active strategy.
Evaluating risk and return

Risk adjusted returns enable us to see how the return was achieved; through stock picking or through taking on risk.
Alpha measures the difference between the actual return and the return expected using CAPM.
A positive alpha suggests good stock selection.
The Sharpe ratio is the excess return of a stock over the risk-free rate, divided by its standard deviation.
It measures return per unit measure of risk.
A higher Sharpe ratio suggests a skilful fund manager, a lower ratio suggests greater risk has been taken to generate returns.
The information ratio evaluates the excess return against the return of the benchmark.
It tells us how good a job the fund manager is doing.

Question 29

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

Sam plans to build his portfolio on the principles of CAPM. What key factor needs to be considered?

Alpha.

Beta.

Covariance.

Standard deviation.

Answer 29

CAPM uses the expected market portfolio return, the risk-free return and Beta in its calculation.

Alpha is a measure of a manager’s stock picking skills; Covariance is linked to correlation and standard deviation is a measure of risk used in the efficient frontier.

Question 30

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

Sam is considering which assets he should choose and has asked you to explain the efficient frontier. You correctly explain that the efficient frontier shows the optimum balance between:

risk and return.

taxation and risk.

return and diversification.

correlation and inflation.

Answer 30

The efficient frontier shows the optimum portfolio for every unit of risk, which is measured by standard deviation.

Question 31

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

Sam decides to invest his additional £50,000 in share Z. In rebalancing his holdings to an equally-weighted portfolio (ignoring the cash element) he should:

increase his weighting in share X by £11,000.

decrease his weighting in share Y by £17,000.

increase his share weighting in Z by £5,000.

keep his weightings in all three unchanged.

Answer 31

The total portfolio value is £50,000 + £39,000 + £70,000 = £159,000.

An equally-weighted portfolio would mean £159,000 ÷ 3 = £53,000 in each stock.

Share X would need to increase from £39,000 to £53,000 i.e. £14,000
Share Y would need to decrease from £70,000 to £53,000 i.e. £17,000
Share Z would need to increase from £50,000 to £53,000 i.e. £3,000

Question 32

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

The correlation between share X and Y is 0.2. This means

they outperform positively correlated assets.

they are offering a good amount of diversification.

the beta of the fund is kept high.

they have a high standard deviation.

Answer 32

they are offering a good amount of diversification.

There are three types of correlation, negative (which provides the widest diversification model), positive and no correlation. Low or negatively correlated assets provide the best diversification.

High beta and standard deviation are high risk, and you cannot say that they would outperform positively correlated.

Note: this is a good example of where you have to pick ‘the best answers from the bunch’ in J12.

It may feel like you’d want to say ‘I need more info…’ but you have to work with what they give you in the question!

Question 33

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

Sam asks you to explain the principles behind the efficient market hypothesis (EMH). You can tell him that…

the availability of information in a large-cap developed market means that it is likely that active managers will outperform the market over the long term.

it is possible to outperform over the long term by selecting undervalued equities in smaller companies.

in a semi-strong market the prices of securities reflects all known information, including private.

weak form EMH is due to the effect of irrational human behaviour on the market.

Answer 33

it is possible to outperform over the long term by selecting undervalued equities in smaller companies.

The key word that makes B right here is ‘smaller’. Smaller companies tend to have fewer analysts researching them so, as there is less information available, the market for smaller companies is less efficient than that of larger companies. This means that it may be possible to identify undervalued securities and outperform over the long term.

Developed markets in large companies are efficient making it unlikely that active managers will outperform.

Private information being reflected in security prices would define strong form EMH, not semi-strong.

EMH is based on the principle that investors act rationally.

Question 34

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

What is the Jensen’s alpha for Share Y?

Answer 34

Jensen’s alpha = actual return – expected return from CAPM.

Expected return = (risky x beta) + risk free
Risky = actual return - risk free

Jensen’s alpha is therefore 10-9 = 1%.

Question 35

Sam is a higher rate taxpayer and has the following portfolio of securities alongside £25,000 held in a deposit account. He has a further £50,000 that he is wishing to add to his investments.

The return on the market portfolio is 7% and the risk-free rate is 3%.

Share X Share Y
Value £39,000 £70,000
Beta 0.8 1.5
Standard deviation 3.5% 6%
Average return 5% 10%
Correlation 0.20

Sam originally invested £55,000 in share X. Despite the loss, he is loath to sell them because he doesn’t want to make the loss ‘real’. This is an example in behavioural finance of:

Prospect theory.

Incorrectly unselected
Anchoring.

Correctly unselected
Regret.

Incorrectly selected
Overconfidence.

Answer 35

Prospect theory or loss aversion is where people are more distressed by losses than they are happy by an equal gain. They avoid selling so that they don’t make the loss ‘real’. This leads to investors holding on to losses for too long, rather than cutting their losses.

Regret would then result if the investment fell further, and they didn’t sell when they had the chance.

Anchoring is where investors will anchor onto numbers they know, such as the original buying price.

Overconfidence is where investors overestimate their own skills.