11. Measuring Portfolio Performance Flashcards
A. Indices (page 2)
Intended to bring together the movements of an individual security and show which direction a market has moved over a period of time.
A1. What are indices used for? (page 2)
- monitoring market performance
- comparing shares with sectors or markets
- comparing fund managers and how they perform
- constructing index funds
- measuring systematic risk (Beta)
Moving averages used to see the short and long-term movements of shares:
- short term moving averages are 20 days or less
- long term moving averages are 100 days or more
A2. Index construction (page 2)
- some indices are more suited for use as benchmarks
- others are better suited to provide short-term information on the movement of the markets
A2A. Weighting of constituents (pages 2 & 3)
MARKET VALUE WEIGHTED INDICES
- majority of the most widely used indices (FTSE 100) are adjusted for ‘free float’
- each index is the summation of the market value (or market capitalisation) of all of the companies within the index
- thus a company with 2x the market capitalisation of a smaller company will have 2x the impact on the index
Issue = companies whose share prices have risen will be a larger part of the index than those that have fallen, so indices will be overweight in those companies whose share prices have risen
A2A. Weighting of constituents (pages 2 & 3)
CONTINUED
FREE FLOAT
- Free Float is the number of shares that are available for trading on the stock market
- companies whose controlling directors hold the majority of shares will be excluded from the free float as these shares are not available to other investors
- the same applies to companies that hold each others shares and again are not available to the public, so excluded from the free float (known as cross-holding)
- founders shares and government holdings are usually excluded too
- The free float more accurately reflects the available supply of shares
A2A. Weighting of constituents (pages 2 & 3)
CONTINUED
PRICE-WEIGHTED INDICES (Dow Jones 30)
- the prices of the included stocks are added together and divided by a divisor, which reflects the number of stocks in the index
- the divisor is adjusted downwards if the company has a stock split, which can happen if it is being successfu; and therefore lead to its weighting in the index actually being reduced!
- price-weighted indices do not make good benchmarks for performance measurement because higher-priced stocks carry more weight than lower-priced stocks
A2A. Weighting of constituents (pages 2 & 3)
CONTINUED
UNWEIGHTED INDICES
- an equal investment in each stock is assumed
- share price and market capitalisation are irrelevant
- a percentagr rise in the share price of any company will have an equal impact on the index
- tend to be used for academic work
A2B. Total return verses capital only (pages 3 & 4)
- Indices can be constructed as total return or capital only
- FTSE, for example, offer both
- CAPITAL ONLY indices reflect price-changes only, and are only useful if the income received is then distributed
- TOTAL RETURN indices should be used in most cases to measure performance
A2C. Limitations of indices (page 4)
- market capitalisation can mean that very large companies can have a big effect on the market and therefore the index they form part of
- if an index reflects changes in capital values only, it is ignoring reinvested dividend income which can make a substantial difference to long-term performance
- do not include transaction costs (buying and selling)
- assume that the investor is fully committed to buying and holds no cash balances
A2D. Benchmark regulation (page 4)
- EU-wide regulation came into effect in 2018 to regulate indices that used as benchmarks
In the eyes of EU Benchmarks Regulation, an index becomes a benchmark if:
- it is used to determine the amount payable under a financial instrument
- it is used to measure the performance of an investment fund, for the purpose of:
1. tracking a return
2. defining the asset allocation of a portfolio
3. computing performance fees
A3. Global indices (page 5)
A3A. FTSE UK Index series (page 5)
- FTSE is now wholly owned by the LSE
- Eight main FTSE indices
FTSE ALL SHARE
- consist of 630 companies
- 98% of UK market capitalisation
- aggregation of FTSE 100, FTSE 250 and FTSE SmallCap indices
- updated in real time
- companies reviewed quarterly
- designed to behave like an actual portfolio and indicator of the London market’s long-term performance
FTSE 100
- 100 largest companies by market capitalisation
- represents 80% of UK market capitalisation
- updated in real time
- companies reviewed quarterly
A3A. FTSE UK Index series (page 5)
CONTINUED
FTSE 250
- next 250 larges companies by market capitalisation after the FTSE 100
- represents 15% of UK market capitalisation
- updated in real time
- companies reviewed quarterly
- has two formats, one that includes and one that excludes investment companies
FTSE 350
- combination of the FTSE 100 and FTSE 250
- covers 95% of UK market capitalisation
- has two formats, one that includes and one that excludes investment companies
- also calculated according to the dividend yield of the constituent companies ranked in descending order
A3A. FTSE UK Index series (page 6)
CONTINUED
FTSE AIM Index Series
- tracks the performance of shares listed on the AIM
- free float
- reviewed quarterly
- there are three main indices:
1. FTSE AIM All-Share Index
2. FTSE AIM 50 (tracks top 50 AIM by market-cap)
3. FTSE AIM 100 (top 100 AIM by market-cap)
FTSE Fledgling
- comprises of companies too small for the FTSE All-Share
- together they represent less than 1% of UK market capitalisation
Other main FTSE Indices
- FTSE UK Gilts Indices
- FTSE Sterling Corporate Bond Index
A3A. FTSE UK Index series (page 6)
CONTINUED
Widely used UK indices
- FTSE All share - for UK Equities
- FTSE Index-Linked (all stocks) - for Index-Linked securities
- FTSE Gilts (all stocks) - for Government securities
A3B. Overseas indices (pages 6 & 7)
DOW JONES INDUSTRIAL AVERAGE (USA)
- takes the share prices of 30 blue-chip companies and measures their movements
- price weighted index (using a divisor)
STAND & POOR’S (S&P) COMPOSITE (USA)
- consists of 500 companies listed on the NY stock exchange
- represents 75% of US market capitalisation
- weighted according to the free float
THE NASDAQ COMPOSITE (USA)
- an index of small young companies
- these companies are usually in technology or biotech
- used as a reference for tech stocks
A3B. Overseas indices (pages 6 & 7)
CONTINUED
NIKKEI 225 (JAPAN)
- based on 225 large, publicly owned Japanese companies
- price-weighted index
TOKYO STOCK PRICE INDEX (TOPIX) (JAPAN)
- provides a better guide to the overall market
- tracks all domestic companies of the exchange’s first section
DAX 30 (GERMANY)
- consists of the 30 larges quoted German companies
- updated in real time
A3B. Overseas indices (pages 6 & 7)
CONTINUED
HANG SENG INDEX (HONG KONG)
- composed of a representative sample of Hong Kong stocks
- is market weighted
CAC GENERAL INDEX (FRANCE)
- records the opening prices of the Paris cash market
CAC 49 (FRANCE)
- updated in real time
- market-value-weighted index of the largest stocks
MSCI WORLD INDEX / FTSE ALL-WORLD INDEX
- are global indices covering global equity markets
B. Measurement of return (pages 7 & 8)
Covering the various measures used by investment managers.
B1. Holding period return (page 8)
DESCRIPTION
HOLDING PERIOD RETURN
- compares returns on different investment
- encompasses the total return, including income and capital gains, over a period
- expressed as a percentage (%) of the original cost
- it equals all income received plus capital gains during the period as a % of the original investment
DISADVANTAGES:
- period looked at must be the same when comparing two investments
- does not take into consideration timing of cash flows or compounding of returns
B1. Holding period return (page 8)
CALCULATION
HOLDING PERIOD RETURN CALCULATION:
D + V1 - V0 R = ------------------- x 100 to get a %
V0
R = holding period return D = income received during the period V0 = price/value at acquisition V1 = price on selling
EXAMPLE:
Investment costs £100, pays a dividend of £10 and is sold for £110 after six months
£10 + £110 - £100 R = ------------------- = 0.20 x 100 = 20%
£100
B2. Relative return (pages 8 & 9)
DESCRIPTION
RELATIVE RETURN
- is the return from an investment/portfolio measured against the return from a benchmark index
- shows how well the investment/portfolio has performed relative to a benchmark
- measures whether a fund manager had added value above the index return
B2. Relative return (pages 8 & 9)
CALCULATION
RELATIVE RETURN CALCULATION:
rREL = r - rB
r = the total holding period return rB = the benchmark return
EXAMPLE:
Portfolio has a total return of 12% and the benchmark rose by 10%
rREL = 12% - 10% = 2%
B3. Money verses time weighted rates of return (pages 9 & 10)
MWR and TWR - incorporate cash inflows/outflows and useful for when cashflows are used
B3A. Money-weighted rate of return (pages 9 & 10)
DESCRIPTION
MONEY WEIGHTED RATE OF RETURN
- a modified form of the holding period return
- adjusts for cash inflows into the portfolio
ISSUES
- not considered appropriate when trying to compare different portfolios
- strongly influenced by the timing of cash flows
- does not identify whether the overall return for the investor is due to the ability of the fund manager or as a result of when additional funds were invested
B3A. Money-weighted rate of return (pages 9 & 10)
CALCULATION
MONEY WEIGHTED RATE OF RETURN CALCULATION
D + V1 - V0 - C MWR = -----------------------
V0 + (C x n / 12)
n = number of months remaining in the year C = the new money introduced during the year V0 = the price or value at acquisition V1 = the price on selling
EXAMPLE
V0 = £20,000 V1 = £24,000 D = nothing as no income paid out Money In = £3,000 in March Money Out = £2,000 in September (withdrawal)
D + V1 - V0 - C MWR = -------------------------------------------
V0 + (C x n / 12) + (C x n /12)
0 + 24,000 - 20,000 - 1,000 MWR = ---------------------------------------------------
[20,000 + (3,000x9/12) + (-2,000x3/12)]
3,000 MWR = --------------------------------- = 0.1379 x 100 = 13.79%
20,000 + 2,250 - 500
B3B. Time-weighted rate of return (pages 10 & 11)
DESCRIPTION
TIME WEIGHTED RATE OF RETURN
- can compare the performance of one fund manager to another by eliminating distortions caused by the timing of new money
- does this by breaking down the return for a particular period into sub-periods
B3B. Time-weighted rate of return (pages 10 & 11)
CALCULATION
TIME WEIGHTED RATE OF RETURN CALCULATION
1 + R = (1 + r1) (1 + r2) (1 + r3) (1 + r4) … (1 + rn)
R = TWR ri = holding period return in each sub-period
EXAMPLE
- Portfolio starting value of £100m
- Value after 6 months is £110m
- £2m cash dividend paid out
- Value at end of 12 moths is £130m
- HOLDING PERIOD
D + V1 - V0 R = ------------------- x 100 to get a % V0
R = holding period return D = income received during the period V0 = price/value at acquisition V1 = price on selling
2 + 110 - 100 r1 = --------------------- = 0.12 x 100 = 12%
100
130 - 110 r2 = --------------------- = 0.1818 x 100 = 18.18%
110
- LINK THE RETURNS TO CALCULATE THE TWR
1 + R = (1 + r1) (1 + r2)
1 + R = (1.12) (1.1818)
1 + R = 1.3236
R = 1.3236 - 1 R = 0.3236 or 32.36% (0.3236 x 100)
B4. Bond yields (page 11)
B4A. Interest Yield (page 12)
DESCRIPTION
BOND INTEREST YIELD
- expresses the annual income from a bond as a percentage of the price an investor would pay for the bond
ISSUES
- can be misleading as bonds may create a capital gain or loss if held until redemption, depending upon the price at which they were purchased
- bonds may trade above or below their par or nominal value because their prices are not fixed
- if the coupon is above current interest rates and the issuer has a strong credit rating, the bond will trade above par
B4A. Interest Yield (page 12)
CALCULATION
BOND INTEREST YIELD CALCULATION:
Coupon Interest Yield = ------------------- x 100
Clean price
Example:
Coupon = 8% Clean price (purchase price) = £124.27
8 6.44% = ------------------- x 100
£124.27
B4B. Redemption yield (pages 12 & 13)
DESCRIPTION
(CALCULATION IN FORMULA SECTION)
BOND REDEMPTION YIELD
- is a more accurate calculation of the yield on a bond
- takes into account the income payments from a bond and the capital gain or loss from holding the bond until maturity
- adjusts the value of each payment according to when it is received
- assumes the bond is held to maturity and that coupons can be reinvested at the redemption yield
- assumes that the investor reinvests each interest payment
B4C. Semi-annual and annual yields (pages 13 & 14)
- semi-annual yields can be doubled to get an annual yield
B4D. Index-linked bonds (page 14)
- calculating a yield for an index-linked bond requires an assumption of the future inflation rate, since the fact value of the bond will increase with inflation
B5. Measuring returns from different asset classes (page 14)
VALUING INVESTMENTS WHERE THERE ARE NO RELIABLE MARKET PRICES AVAILABLE
- broker quotes can be used for OTC derivatives
- models can be used to value derivatives
WHEN AN INVESTMENT IS GEARED, AS IS OFTEN THE CASE WITH PROPERTY, THE GEARED AND UNGEARED RETURN MAY BE QUOTED
- unleveraged return only shows the return of the original investment
- leveraged return includes the effect of the leverage and typically gives a larger rise or fall
IN SOME ASSET CLASSES, IRR RATHER THAN TWR IS COMMONLY USED TO ASSESS PERFORMANCE
- for private equity, the fund manager, rather than the client, often commits to making additional investments in a company and therefore a TWR is not appropriate
NO SUITABLE BENCHMARK
- for alternative investments, there may be no suitable benchmark against which to measure performance
C. Risk-adjusted returns (pages 14 & 15)
There are various ways to measure risk-adjusted returns
C1. Sharpe Ratio (pages 14, 15 & 16)
DESCRIPTION
SHARPE RATIO
- is a measure of the risk-adjusted return of a stock
- measures the excess return for every unit of risk that is taken in order to achieve the return
WHAT IT MEASURES
- the higher the sharpe ratio the better the return on an investment compensates an investor for the risk taken
i. e. the better it’s risk-adjusted performance has been - a negative sharpe ratio indicates that a risk-free asset would have performed better
C1. Sharpe Ratio (pages 14, 15 & 16)
CALCULATION
SHARPE RATIO CALCULATION:
standard deviation of the return on the investment
EXAMPLE:
Return = 10%
Risk-free return = 4%
Standard Deviation = 8%
10 - 4 Sharpe Ratio = ------------ = 0.75 (or 0.75%)
8
Portfolio earned a 0.75% return above the risk-free investment.
C2. Alpha (pages 16 & 17)
DESCRIPTION
ALPHA (JENSEN’S ALPHA)
- the difference between the return that would be expected from a security, given its beta, and the return it actually produced
- is the part of a return that cannot be explained by movements in the overall market
- sometimes referred to as ‘value added’
WHAT IT SHOWS
- positive alpha shows that the investment has performed better than expected given its beta
- negative alpha indicates that it has performed worse than expected given its beta
i. e. for a portfolio it allows us to quantify the value added or taken away by a manager through active management
C2. Alpha (pages 16 & 17)
CALCULATION
ALPHA CALCULATION
a = actual portfolio return - [Rf + Bi (Rm - Rf)]
BODMAS: 1. Rm - Rf 2. Bi x (Rm - Rf) etc
Rf = risk-free rate of return
Rm = market return
Bi = beta of the fund or portfolio
EXAMPLE
Portfolio return = 12%
Beta of fund = 1.5
Market return = 8%
Risk-free rate = 2%
C3. Information ratio (pages 17 & 18)
DESCRIPTION
INFORMATION RATIO
- used to assess the risk-adjusted performance of active portfolio managers
- shows the consistency to which they beat the benchmark index
- measures the relative return achieved by an investment manager divided by the amount of risk the manager has taken relative to a benchmark
NEGATIVE INFORMATION RATIO
- investor would have received a better return by matching the benchmark using tracker fund
C3. Information ratio (pages 17 & 18)
CALCULATION
INFORMATION RATIO CALCULATION
Rp - Rb Information Ratio = -------------------------
tracking error
Rp = portfolio return Rb = benchmark return
EXAMPLE
Fund return = 13%
Benchmark return = 10%
Fund tracking error = 6%
13 - 10 Information Ratio = ------------------------- = 0.5
6
Chapter 11 Key Points (pages 19 & 20)
INDICES
- can be used to monitor market performance
- can be used to compare the performance of a particular stock with its sector or a market
- can be used to construct index funds
- can be constructed in different ways:
1. price-weighted
2. equal-weighted
3. market capitalisation-weighted (most common) - most indices are capital-only, but some are total-return
- bond indices are usully weighted by the market value of the bond issue
- FTSE 100 is 80% of UK market-capitalisation
- FTSE All Share is 97% of UK market-capitalisation
Chapter 11 Key Points (pages 19 & 20)
CONTINUED
MEASUREMENT OF RETURN
- total return measures the capital and income return from an investment
- relative return compares a return to a benchmark
- two methods used to measure portfolio performance:
1. MWR
2. TWR (eliminates time created distortions) - the interest yield measures the income derived from a bond as a percentage of the clean price but does not take account of any capital gain or loss if the bond is held until redemption
- measuring returns from assets sometimes needs to take into account the lack of reliable market prices
Chapter 11 Key Points (pages 19 & 20)
CONTINUED
RISK-ADJUSTED RETURNS
- sharpe ratio compares different risk-reward options
1. the higher the sharpe ratio, the better an investment compensates an investor for the risk taken - alpha measures the return that would be expected from a security, given its beta, compared to what it acheived
1. is a measure of the manager’s stock-picking skill - information ratio assesses the risk-adjusted performance of active portfolio managers
1. used to gauge the skill of a fund manager and shows the consistency at which they beat the benchmark
