13. Assessing investment performance Flashcards
“past performance is not necessarily a
guide to future performance” however…
We know that:
* UK equities tend to outperform UK deposits and bonds over the medium
to long term
3 Basic performance measures
- The time value of money
- Compounding & Discounting
- Real & Nominal terms
Time Value of Money - a recap
Definition: Money received today is worth more than the same amount in the future due to its earning potential.
Future Value (FV):The amount a sum of money today will grow to, given a specific interest rate over time.
- Example: £1 today at 5% interest will be worth £1.05 in a year.
Present Value (PV): The current worth of a future sum of money, discounted by the interest rate.
- Example: A promise of £1.05 in 12 months has a present value of £1 today.
Compensation for Delay: Receiving money later must come with compensation, like interest or growth.
Practical Example: Retailers offering “buy now, pay later” allow the buyer to:
- Earn interest or growth on their money before making the payment.
- Benefit from inflation reducing the real value of the debt over time.
Main Implication: A single sum or series of payments can be converted to an equivalent value today or calculated for its future value.
Compound interest and discounting - a recap
Simple Interest: Interest calculated only on the original capital each year.
- Example: £1,000 at 4% simple interest = £40 per year.
- After 3 years: £1,120 total.
Compound Interest: Interest is added to the capital, and future interest is earned on both the capital and the interest.
- Example: £1,000 at 4% compound interest = £1,040 after 1 year, £1,081.60 after 2 years, £1,124.86 after 3 years.
Discounting: The reverse of compounding, used to determine how much to invest now to achieve a future target sum.
- Example: To reach £15,000 in 8 years with a 6% return, you discount the future amount by 6% each year to find the present investment needed.
Application: Both simple and compound interest principles apply to any percentage return, including capital growth.
Real and nominal terms - a recap
Nominal Rate of Return: The stated interest rate or return, without adjusting for inflation.
* Example: 5% nominal return on a deposit account.
Real Rate of Return: The nominal rate adjusted for inflation.
* Example: 5% nominal rate with 3% inflation = 2% real return.
Tax Impact: The real return may be further reduced by taxes.
- Example: A basic-rate taxpayer earning 5% interest with 3% inflation has a net nominal return of 4%, and a net real return of 1%.
- For a higher-rate taxpayer, real return can be nil if inflation equals the post-tax nominal rate.
Holding period return - What is it? When is it used? and how is it calculated?
13.3 Measuring the return
Holding Period Return (HPR):Measures the total investment return (income + capital growth) over a specific period, expressed as a percentage of the original investment.
* Used for comparing returns over the same or different periods.
* Annualisation: HPR can be annualised for investments held over different periods.
Formula:
HPR= (I + (C1 -C0) ÷ C0) x 100
Where
* I = Income received (e.g., dividends).
* C0 = Original investment.
* C1 = Final investment value.
Example:
Bought shares for £100, sold for £110, and received £4 dividends.
= 14%
Annualising the return (holding returns) - Why? How is it useful? How to calculate?
Assumptions?
Annualising Returns: Allows comparison of investments with different holding periods by assuming consistent returns over time.
Why Annualise?: To compare returns on an equal basis, especially when investments are held for different durations.
Key Assumption: Assumes the same rate of return over all periods, which may not always hold true but provides a useful comparison.
Formula:
(1+r)*n =1+R
Where:
* r = Return for the holding period.
* n = Number of holding periods in a year.
* R = Annualised return
Example:
* A 14% return over six months: (1.14 × 1.14) = 1.30 = 30% annualised return.
* A 5% return over three months: 1.05^4 = 1.215 = 21.5% annualised return.
Time‑weighted rate of return - Definition? Why? and calculation?
benefit?
Definition: TWR measures the compound rate of return for a unit of money over a given period, dividing returns into equal sub-periods, allowing for comparison when cash flows occur at different times.
Why Use It?: TWR is ideal for comparing investment fund performance, as it eliminates the impact of money entering or leaving the fund, focusing on how well the money was managed.
Calculation Example:
* Investment over 4 quarters with returns of 4%, 7%, 6%, and 8%.
* To find the TWR: 1.04 x 1.07 x 1.06 x 1.08 = 1.274 or 27.4% compounded return over the period.
GIPS Requirement: Funds must use TWR to comply with Global Investment Performance Standards (GIPS), ensuring standardized performance reporting.
Benefit: TWR isolates the manager’s investment performance, unaffected by timing of cash flows into or out of the fund.
Three ways that the risk-adjusted return can be shown?
- The Alpha
- The Sharpe ratio
- The information ratio
The alpha - recap: Definition, purpose, application, limitation?
What does a positive and negative alpha show?
13.4 Risk‑adjusted returns
Definition: Alpha measures the risk-adjusted return of a share or collective fund compared to a benchmark (typically an index).
Purpose: It shows the difference between the actual return and the expected return, based on the security’s beta (volatility measure).
Interpretation:
- A positive alpha (e.g., 3%) indicates that the investment outperformed the benchmark by 3%, suggesting the additional risk was worth taking.
- A negative alpha means the investment underperformed the benchmark, implying the risk was not justified.
Contrast with Beta: While beta measures how much a security moves with the market, alpha shows how much it moves independently of market fluctuations.
Application: Often seen as a measure of a manager’s stock selection skills, though it may also reflect luck.
Limitation: Both alpha and beta are based on past performance, so they are not always reliable for predicting future outcomes.
The sharpe ratio? - Definition, formula, advantages, interpretation, etc.
13.4 Risk‑adjusted returns
Definition: The Sharpe ratio measures how well an investment’s return compensates for the risk taken, comparing it to a risk-free investment (e.g., Treasury bills).
Formula:
- (Return - Risk free return) ÷ Standard deviation
Example: If a unit trust has a return of 7%, a standard deviation of 5%, and the risk-free return is 3%, the Sharpe ratio is:
- (7-3) ÷ 5 = 0.8
This means the investment provided 0.8% return per unit of risk above the risk-free rate.
Advantages:
* Does not rely on beta, making it more reliable as standard deviation is considered more accurate.
* Allows comparison between different types of securities using the same calculation.
Interpretation:
* A higher Sharpe ratio indicates better returns for the same level of risk.
* Good returns and low standard deviation result in a high Sharpe ratio, while high standard deviation needs higher returns to maintain a strong Sharpe ratio.
Comparison Use: The Sharpe ratio is only meaningful when compared with other investments.
The information ratio? - Definition, formula, advantages, interpretation, etc.
13.4 Risk‑adjusted returns
Definition: The Information Ratio (IR) measures risk-rated return, comparing a fund’s return to a chosen benchmark (not a risk-free rate, unlike the Sharpe ratio).
Formula:
* (Fund return - Benchmark return) ÷ tracking error
Tracking error: Measures how closely a fund follows its benchmark.
Performance Scale:
* 0.5 = Good performance
* 0.75 = Very good
* 1.0 = Excellent
Usage:
- Useful for evaluating funds with similar asset allocation.
- Positive IR indicates a manager’s ability to outperform the benchmark and suggests better stock-picking skills.
Interpretation:
* Higher IR implies better fund performance relative to its benchmark, often outperforming average fund managers.
Stock market indicies - What is it? What are they useful for?
Definition: Stock market indices measure the combined price movements of a range of shares to show the performance of a market or sector over time.
Uses for Investors:
- Compare performance of shares or investments with the overall market or specific sectors.
- Identify market trends and potential future movements.
- Compare fund performance against a benchmark index.
- Help analysts observe economic activity.
Types of Indices: Not limited to shares—include property, gilts, bonds, and other assets like art.
Limitations:
- Weighted indices can be distorted by large companies.
- Most indices focus on capital returns, excluding dividends (underestimating total returns).
- No consideration of transaction costs or tax.
- Global companies listed on multiple exchanges can distort the index’s reflection of a country’s economy.
Summary of the main stick indicies - FSTE 100, FTSE All-share
FTSE 100
* Composition: 100 largest UK companies by share capitalisation.
* Real-Time Index: Updates during the day with price changes.
* Market Capitalisation Weighting: Companies’ influence on the index is based on their market cap (e.g., AstraZeneca at 8.64%).
* Significance: Represents around 81% of UK total market capitalisation.
* Impact of Changes: Significant share price movements (e.g., AstraZeneca) can greatly influence the index, while smaller companies (e.g., BT) have less impact.
* Relegation/Promotion Effects: Losing/gaining FTSE 100 status affects market confidence and share price due to tracker fund adjustments.
FTSE All-Share
Composition: Includes all companies in FTSE 100, FTSE 250, and FTSE Small Cap.
Coverage: Represents around 99% of UK market capitalisation across 38 sectors.
Indicator: Good indicator of the London market’s long-term performance.
Calculation: Not a real-time index; value calculated at the end of each business day.
Summary of the main stick indicies - Dow-Jones, NASDAQ, NIKKEI 225
Dow Jones Industrial Average (DJIA)
* Composition: 30 of the largest and widely held blue-chip companies on the New York Stock Exchange.
* Purpose: Represents major segments of the U.S. economy.
NASDAQ Composite Index
* Composition: Approximately 3,000 companies listed on the NASDAQ stock exchange.
* Technology Focus: More than 50% weighting in technology stocks, making it a key indicator for the tech sector.
* Global Scope: Includes companies outside the USA.
Nikkei 225
* Composition: Index for the Tokyo Stock Exchange, comprising 225 Japanese stocks.
* Unweighted Index: Based on the average price of the constituent stocks, rather than market capitalisation.
