CISI
Chartered Wealth Manager Programme
Portfolio Construction Theory – Day 1
Cris Glascow
1
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Objectives
By the end of the workshop you will have:
 Revised learning outcomes 1, 2 and 3
 Practised exam type questions
 Identified areas you need to read about more
thoroughly
 Devised an action plan.
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Agenda





The Portfolio Construction Theory exam
Module 1
Module 2
Module 3
Review.
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General points about the Portfolio
Construction Theory exam:
There are 3 sections to the exam:
 Section A – 20 multiple choice questions - 20
marks
 Section B – Short written questions worth 3 to 6
marks each in total - 40 marks
 Section C - 2 case studies from a choice of 3 worth
20 marks each - 40 marks
 Pass mark at least 50%
 Pass rate 59% December 2015 (44% June 2015)
 You will be using the 2015/16 tax tables.
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5 point plan to do well in this exam:
1.
2.
3.
4.
5.
Know the material
Understand the concepts
Be able to apply it to scenarios and case studies
Plan your study time
Practise answering questions.
Ref: Exam tips http://glascow.co.uk/how-can-you-pass-the-cisisportfolio-construction-theory-exam/
http://glascow.co.uk/benefits-of-structured-study-topass-an-exam/
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Module 1 – Fundamentals of
investment theory
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Investment objectives and client
circumstances
EXAM PRACTICE QUESTION –
Briefly describe four different types of
investment objective.
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Investment objectives and client
circumstances
Client circumstances
 Financial needs and preferences
 Risk appetite
 Constraints.
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Indifference Curves
Return %
A
B
Which investor is
more risk averse?
Risk σ
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Risks of investments
Scenario: List and discuss the types of risk an
investor will be exposed to by holding shares in a
UK listed company with significant UK and
overseas operations.
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Reducing the impact of investment
risks
 Diversify across asset classes
 Diversify across sectors
 Diversify across geographic areas
 Diversify across different fund/investment
managers.
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Probability of returns
One-year
return
R (%)
8
Probability
P
0.2
Weighted
probability
RxP
1.6
12
16
25
0.3
0.3
0.2
3.6
4.8
5
Total
15
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The variance of returns
Example:
Investments ABC and PQR have the following possible returns and
probabilities of those returns:
Investment ABC
One year return
R (%)
10.0
14.5
15.0
Probability
P
0.15
0.30
0.55
Expected return
Weighted
probability
R x P (%)
1.5
4.35
8.25
14.1
Investment PQR
One year return
R (%)
-20.0
16
30
Probability
P
0.15
0.6
0.25
Expected return
Weighted
probability
R x P (%)
-3.0
9.6
7.5
14.1
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Standard Deviation
 The standard deviation of returns measures how widely
the actual return of an investment year on year varies
around the mean or expected return (as explained
previously).
 Where an investment has year on year returns that are
close to its expected return, it is said to have a low
standard deviation.
 Where returns vary widely, the overall expected returns
may be the same as the investment with a low standard
deviation, but it will be higher risk (returns fluctuate to
greater extremes).
 The example on the previous slide demonstrates that
investment PQR has a higher standard deviation than
investment ABC.
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Standard Deviation
Example: PQR plc - Mean average return: 14.1%
Return
Difference from
the mean (14.1)
-20.0
16
30
-34.1
1.9
15.9
Difference
Squared
1162.81
3.61
252.81
Difference
squared
multiplied by
the probability
174.4215
2.166
63.2025
239.79
The standard deviation will be the square root of 239.79 = 15.48
(rounded down)
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Standard deviation
Example: PQR plc - Mean average return: 14.1%
The standard deviation is 15.48. Roughly 68% of the time, returns will
be between -1.38% and 29.58% (1 SD). Approximately 95% of the time
, returns will be anywhere between -16.86% and 45.06% (2 SDs).
Nearly all the time, returns will be within 3 SDs. Note distribution curve
below:
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Standard deviation
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Investment returns
 Arithmetic mean
 Median
 Mode
 Weighted mean
 Geometric mean.
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Expected returns when combining
assets
 Expected return of a portfolio is the weighted average of the
returns from each security included.
 Expected return = pArA + (1 - p)rB
Where:
 pA is the proportion of the portfolio allocated to security A
 1 - p is the proportion of the portfolio allocated to security B
 r is the expected return from each security.
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Covariance
If two items tend to vary together, you
analyse their covariance
Covariance can be positive or negative.
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Correlation
How the change in one item effects a
change in another item within a scale of
between minus -1 to +1.
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Variance of Investment X
Sample set of returns of X (in %):
4, 2, 4, 6, 4, 2, 4, 6
Average returns of X: 4
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Variance of Investment X
Return – Ave Return
Difference
Difference Squared
Total
Variance
Standard deviation
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Variance of Investment X
Return – Ave Return
Difference
Difference Squared
(4 – 4)
(2 – 4)
(4 – 4)
(6 – 4)
(4 - 4)
(2 – 4)
(4 – 4)
(6 – 4)
Total
Variance
Standard deviation
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Variance of Investment X
Return – Ave Return
Difference
(4 – 4)
0
(2 – 4)
-2
(4 – 4)
0
(6 – 4)
2
(4 - 4)
0
(2 – 4)
-2
(4 – 4)
0
(6 – 4)
2
Difference Squared
Total
Variance
Standard deviation
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Variance of Investment X
Return – Ave Return
Difference
Difference Squared
(4 – 4)
0
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
(4 - 4)
0
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
Total
16
Variance
Standard deviation
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Variance of Investment X
Return – Ave Return
(4 – 4)
Difference
0
Difference Squared
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
(4 - 4)
0
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
Total
16
Variance
16 / (8 -1)
2.29
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Variance of Investment X
Return – Ave Return
Difference
Difference Squared
(4 – 4)
0
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
(4 - 4)
0
0
(2 – 4)
-2
4
(4 – 4)
0
0
(6 – 4)
2
4
Total
16
Variance
16 / (8 -1)
2.29
Standard deviation
√ 2.29
1.51
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Variance of Investment Y
Sample set of returns of Y (in %):
10, 15, 10, 5, 15, 15, 5, 5
Average returns of Y: 10
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Variance of Investment Y
Return – Ave Return
Difference
Difference Squared
(10 – 10)
0
0
(15 – 10)
5
25
(10 – 10)
0
0
(5 - 10)
-5
25
(15 – 10)
5
25
(15 - 10)
5
25
(5 - 10)
-5
25
(5 - 10)
-5
25
Total
150
Variance
150 / (8 -1)
21.43
Standard deviation
√ 21.43
4.63
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Covariance of Investments X and Y
Return – Ave Return X Return – Ave Return Y
Sum of Return – Ave
Return X multiplied by
Return – Ave Return Y
Total
Covariance XY
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Covariance of Investments X and Y
Return – Ave Return X Return – Ave Return Y
Sum of Return – Ave
Return X multiplied by
Return – Ave Return Y
(4 – 4)
(2 – 4)
(4 – 4)
(6 – 4)
(4 - 4)
(2 – 4)
(4 – 4)
(6 – 4)
Total
Covariance XY
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Covariance of Investments X and Y
Return – Ave Return X Return – Ave Return Y
(4 – 4)
(10 – 10)
(2 – 4)
(15 – 10)
(4 – 4)
(10 – 10)
(6 – 4)
(5 - 10)
(4 - 4)
(15 – 10)
(2 – 4)
(15 - 10)
(4 – 4)
(5 - 10)
(6 – 4)
(5 - 10)
Sum of Return – Ave
Return X multiplied by
Return – Ave Return Y
Total
Covariance XY
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Covariance of Investments X and Y
Return – Ave Return X Return – Ave Return Y
Sum of Return – Ave
Return X multiplied by
Return – Ave Return Y
0
(4 – 4)
(10 – 10)
(2 – 4)
(15 – 10)
-10
(4 – 4)
(10 – 10)
0
(6 – 4)
(5 - 10)
-10
(4 - 4)
(15 – 10)
0
(2 – 4)
(15 - 10)
-10
(4 – 4)
(5 - 10)
0
(6 – 4)
(5 - 10)
-10
Total
-40
Covariance XY
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Covariance of Investments X and Y
Return – Ave Return X Return – Ave Return Y
Sum of Return – Ave
Return X multiplied by
Return – Ave Return Y
0
(4 – 4)
(10 – 10)
(2 – 4)
(15 – 10)
-10
(4 – 4)
(10 – 10)
0
(6 – 4)
(5 - 10)
-10
(4 - 4)
(15 – 10)
0
(2 – 4)
(15 - 10)
-10
(4 – 4)
(5 - 10)
0
(6 – 4)
(5 - 10)
-10
Total
-40
Covariance XY
-40 / (8 -1) =
-5.71
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Correlation between Investments X and Y
Covariance XY
------------------------SD of X x SD of Y
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Correlation between Investments X and Y
-5.71
--------------1.51 x 4.63
= -0.81
Handout 1 – Correlation Exercise
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Portfolio volatility
Assuming that two securities are combined in a portfolio and that we
know the standard deviation of each and the covariance of returns for
the combined securities, we can calculate the expected risk of the
portfolio. The formula for this is:
sr² = pa² sa² + pb² sb² + 2 pa pb Cov(ra,rb)
Where:
 sa and sb are the standard deviations of the securities A and B
 sa² and sb² are the variances of the securities A and B
 pa and pb are the proportions of the portfolio allocated to securities A and B
 Cov(ra,rb) is the covariance of returns between securities A and B
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Portfolio volatility
Beta
What does it show?
How can it be calculated?
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Portfolio volatility
Value at Risk (VAR)
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Portfolio volatility
Value at Risk (VAR)
VaR = Expected Return – Portfolio Volatility x tstatistic for the confidence interval
t-statistic
% of values
Confidence level
1
68
84%
1.282
80
90%
1.645
90
95%
1.960
95
97.5%
2.326
98
99%
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Portfolio volatility
Value at Risk (VAR)
 A client is considering investing in XYZ plc but is
concerned about the possible downside in the
coming month.
 The shares have a mean return of 0.7% per month
and a monthly standard deviation of 0.075
 What is the expected loss at a 95% confidence
level?
Handout 2 – VaR Exercises
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Pound cost averaging
Meaning
Advantages and disadvantages compared
to lump sum investment
Using value averaging as an alternative.
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Pound cost averaging
 Regular investment into a share or a fund of a
level amount over a given period
 When prices are low, more shares or units are
bought
 When prices are high, less shares are bought
 As a result, the average price paid for shares or
units is less than the average price of the
shares over the same period.
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Practice Question
Over a four month period, an investor buys:
110 units at £1.00
125 units at 90p
160 units at 80p
40 units at £1.30
a) Calculate
i) the average prevailing price of the units
ii) the average price paid for the units
b) Briefly explain what is meant by ‘pound cost averaging’
and whether or not it is represented by the investment
policy in a).
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Fundamentals of Investment Theory
EXAM PRACTICE QUESTIONS 1. What are the main socio-economic
characteristics that are expected to influence
risk tolerance? (2 marks)
2. Why are equities considered a high risk asset
class? (3 marks)
3. Explain why indifference curves of a more risk
averse investor have a steeper slope that those
of a less risk averse investor. (3 marks)
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Module 2 – Principal Asset Classes
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Cash deposits
 Deposit-taking institutions are of varying
creditworthiness; default risk must be
assessed
 Inflation reduces returns and could mean the
real return after tax is negative
 Interest rates change and so the returns from
cash deposits will vary
 There will be currency risk, and different
regulatory regimes to take into account,
where funds are invested offshore
 Commercial and private banks, building
societies and NS&I.
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Annualised rate of interest
Example:
 Account pays interest at an annual rate of 3.8%
 Interest is credited half-yearly
 3.8% / 2 = 1.9% will be paid half-yearly
 The annualised rate is: [(1 + 0.019)2 - 1] = 0.03836
 0.03836 x 100 = 3.84% (rounded).
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Tax treatment of cash deposits
 No capital gains tax
 Interest taxed at 10%, 20%, 40% or 45% of
gross interest
Example: In 2015/16, Jane receives interest of
£900.00 net from her bank deposit account. She
is a 45% tax payer. Calculate the additional tax
she will have to pay on the interest via her selfassessment tax return.
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Cash ISA
 Minimum age 16
 Cash ISA limit is £15,240
 Junior ISA limit is £4,080
 Savings must be made by 5 April to apply to
relevant tax year
 Unused savings cannot be rolled over to a
subsequent tax year.
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Money markets
 Short-term lending / borrowing typically up to 12
months
 No centralised exchange
 Benchmarking to LIBOR
 Convention to issue in bearer form
 Often no coupon - discount to maturity value
provides yield
 Repos
 Money market participants.
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Money market instruments - Treasury Bills
 Short-term loan instruments. Guaranteed by UK
government
 28 days, 91 days, 182 days or 364 days to redemption
 No coupon - issued at a discount to maturity value
 Issued by DMO
 Can be held in CREST and Euroclear
 Competitive weekly tenders - min £500k nominal. Above
this bids in multiples of £50k
 Subsequent trading - minimum denomination is £25k
 Primary participants – banks who also provide secondary
market dealing levels.
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Calculating yields on Treasury Bills
Example:
Yield =
100 - discounted value
---------------------------------------discounted value x Days / 365
e.g.
100 - 99
---------------------- = 0.020258 or 2.0258%
99 x 182/365
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Offshore deposits
 Interest credited gross. Tax consequences
 Key risks of offshore deposits.
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Effects of inflation on deposit
interest
Example:
Calculate the real returns of
a deposit that generated 4%
nominal over one year when
inflation was at a rate of
2.5% pa over the same
period.
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Fixed interest securities
 Basics
 Borrowers (issuers)
 Bonds are negotiable instruments.
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Fixed interest securities - Features
 Maturity dates
 Coupon
 Coupon frequency
 Spreads
 Stripped bonds.
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Fixed interest securities – Corporate
Bonds
 Markets
 Redemption
 Credit ratings and
security
 Convertible bonds and
warrants.
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Risks associated with fixed interest
securities
 Interest rate
 Inflation
 Default
 Liquidity
 Political
 Issue specific
 Fiscal.
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Bond Sensitivities
Impact of:
 Coupon
 Yield
 Term to maturity.
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Macaulay Duration and its
Determinants
What is Macaulay Duration?
Determinants.
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Calculation of Macaulay Duration
Bond price
£100.00
Yield to maturity (YTM)
3.0%
Face value
£100.00
Coupon frequency
1
Coupon rate
2.00%
Life in years
5
Period
Cash Flow
PV Cash Flow
Duration calculation
Cash Flow/ [(1 +
YTM/Coupon
Frequency)^Period]
PV Cash Flow * Period
1
£2.00
£1.94
£1.94
2
£2.00
£1.88
£3.76
3
£2.00
£1.83
£5.49
4
£2.00
£1.78
£7.12
5
£102.00
£87.99
£439.95
TOTALS
£95.42
£458.26
Macaulay Duration
£458.26 / £95.42
4.802
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Modified Duration
Formula: Macaulay Duration / 1 + YTM
Gives an approximation of how much a bond’s
price will move for a % change in yield.
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Convexity
*
* Convexity Error
Price
Actual Price
*
Predicted Price
Yield
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Equities
Value of a share
Distribution of profits
Gains.
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Equity prices
 Influences on share price movements
Ref – Equity performance:
http://forecast-chart.com/historical-ftse-100.html
 Efficient Market Hypothesis
 Technical analysis
 Behavioural finance
 Equities within a portfolio.
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Share Valuation Models
Dividend Discount Model:
P0 = Σ [Dt / (1 + k)t]
Where:
 P0 is the price of the share;
 Dt is the dividend paid at year t (t =1 to infinity);
 k is the return demanded by shareholders in the
firm.
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Share Valuation Models
Price / Earnings Multiple:
P0 / E = (1-b) / (k – br)
Where:
 (1-b) is the proportion of earnings paid as a
dividend;
 b represents the proportion of earnings reinvested;
 r represents the return on equity based on the
reinvested earnings.
 k is the return demanded by shareholders in the
firm.
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Algorithmic trading
Definition
Advantages to traders.
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Types - Ordinary and Preference Shares
Ordinary
Preference
Voting rights
Dividends
Order of payment
Taxation
Other types
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Contracts for difference (CFD’s)
 Traded Over The Counter (OTC) with a provider
 Agreement between two parties to exchange the
difference between the opening price and the closing
price of a contract, at the close of the contract multiplied
by some underlying specified size of the contract
 Can be traded on a variety of underlying: stocks, indices,
commodities
 Cost effective – no stamp duty and avoid commission of
buying or selling shares
 Allow you to go short without stock borrowing
 But unlike spread betting, CGT is payable on realised
gains.
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Commodities
Exercise:
1. Explain using examples, the main characteristics
and uses of hard and soft commodities
2. List the advantages of indirect investment into
commodities.
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Property
Direct investment types
Commercial - retail units / offices
Industrial
Farmland / Woodland.
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Property
Buy to let
Factors in choosing buy to let property
Types of Returns
Advantages and disadvantages of buy to
let.
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Module 3 – Collective Investments
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Unit trusts, OEICs and investment
trusts
Exercise:
In your groups complete the following
worksheet comparison of unit trusts, OEICs
and investment trust companies.
Handout 3 – UT/OEICs/ITCs
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Hedge funds
Exercise:
1. What are the main features, potential advantages
and risks of hedge funds to investors?
1. Identify and explain 6 different hedge fund
strategies.
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Investment trusts
Exercise:
Complete the following questions relating to
investment trusts.
Handout 4 – Investment Trust Companies
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Venture Capital Trusts
Exercise:
Identify which of the following statements
relating to venture capital trusts are true and
which are false.
Handout 5 – VCTs
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Exchange Traded Products (ETPs)
 What?
 Costs?
 Similarities with other investments.
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Offshore funds
Structure
Reporting or non-reporting funds
Advantages and disadvantages.
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Day 1 Review
 Review slides and exercises against syllabus
 Check areas of understanding - questions for
next session
 Assess past exam reports for questions on
syllabus areas covered.
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