Calculations Flashcards
CAPM Calculation
E (R) = Rf + β (E(Rm) - Rf)
Rf = Risk Free Return
β = Beta
E(Rm) Expected Market Return
C.A.P.M
Links the expected return of an investment to its Beta
Effective Rate of Interest (A.E.R.)
R = (1 + i/n)n - 1
R = Effective annual rate, i = Nominal rate n = Number of compounding periods per year (for example, 12 for monthly compounding):
Effective Rate of Interest (A.E.R) - Example
R = (1 + i/n)n - 1
Nominal Rate is 3.2% P.A compounded on a QTR (4 payments) basis. £100 Invested 3.2% / 4 = 0.008 1+0.008 = 1.008 1.008 (To the power of 4) = 1.032 1.032 - 1 = 0.03238 0.03238 * 100 = 3.24%
Time Value of Money - Accumulation of Money
Amount (1 + r)n
r = Interest rate n = Time Period * this is to the power
Annualised rate of return
PV (1 + r)n = FV
PV = Present Value r = rate of return n = number of time periods * this is to the power
Annualised rate of return - Example
PV (1 + r)n = FV
PV = £3,000 FV = £3,383 in 4 years time
r = £3,383 / £3,000 = 1.1276
- 1276 √4 = 1.0304
- 0304 - 1 = 0.0304
- 0304 = 100 = 3.04%
Working Capital
Working Capital = Current Assets / Current Liabilities
Links back to changes in Assets and Liabilities
Good measure of resilience and efficicency
Operating Profit Margin
Operating Profit Margin = Operating Income (EBIT) / Sales Revenue * 100
Operating Profit Margin - Example
Operating Profit Margin = Operating Income (EBIT) / Sales Revenue * 100
Operating Income = £12,000,000
Sales Revenue = £170,000
12,000,000 / 170,000,000 = 0.070588
0.070588 * 100 = 7.06% (2 DP’s)
Working Capital Ratio
Working Capital Ratio
Current Assets / Current Liabilities
Current Assets £61,200,000
Current Liabilities £27,600,000
£61,200,000 / £27,600,000 = 2.22 (2 DP’s)
Increase in Revenue
Increase in Revenue
(Current Year - Previous Year)/Previous Year * 100
Increase in Revenue - Example
Increase in Revenue
(Current Year - Previous Year)/Previous Year * 100
Current Year = £150,000
Previous Year = £125,000
£150,000 - £125,000 = £25,000
£25,000 / £125,000 = 0.20
0.20 * 100 = 20%
Increase in Revenue = 20%
Return on Equity (ROE)
Profit / Total Equity
Return on Capital Employed (ROCE)
ROCE
Operating Profit x 100%) / (Capital Employed = Equity + Long term borrowing
ROCE - Notes
The return on all assets including debt
ROE is just the equity investment
Profit figure normally includes interest
A low return on assets should prompt investors to ask if management is making the best use of capital available.
ROCE is especially useful when comparing the performance of companies in capital-intensive sectors such as utilities and telecoms. This is because unlike other fundamentals such as return on equity (ROE), which only analyzes profitability related to a company’s common equity, ROCE considers debt and other liabilities as well. This provides a better indication of financial performance for companies with significant debt.
Adjustments may sometimes be required to get a truer depiction of ROCE. A company may occasionally have an inordinate amount of cash on hand, but since such cash is not actively employed in the business, it may need to be subtracted from the Capital Employed figure to get a more accurate measure of ROCE.
TWR Time Weighted Returns
Time Weighted Returns
Transaction
V1 V2
—- —–
V0 (V1 +/- C)
V0 = Original Value
V1 = Value at end of period 1
V2 = Value at end of period 2
(V1 +/-C) Value at end of period 1 plus or minus contribtuion
TWR Time Weighted Returns - example
Time Weighted Returns
V1 V2
—- X —– - 1
V0 (V1 +/- C)
Original Value = £18,000
Value at end of period 1 = £19,000
Value at end of period 2 = £20,100
Contribution £1,000
£19,000 / £18,000 = 1.055
£20,100 / £20,000 = 1.005
- 055 * 1.005 = 1.0603
- 0603 - 1 = 0.0603
- 0603 * 100 = 6.03% (2 DP’s)
Dividend Yield
Dividend Yield
Dividend Per Share / Market Price of Share
Dividend Yield Notes
High Yield Little expectation of growth Losses / Insolvency Negative Capital Growth Special Dividend
Dividend Cover
Dividend Cover
Post Tax Profit / Dividend Paid (to ordinary shareholders)
Rights Issue - Rights Premium
Rights Issue - Rights Premium
Ex Rights Price - Issue Price
Rights Issue - Rights Premium - Example
Rights Issue - Rights Premium
Ex Rights Price - Issue Price
Ex Rights Price £350
Issue Price £320
£350 - £320 = £30
Rights Issue
Rights Issue
1 for 3 rights issue at 320
Current Price 360
Existing Value 3 * 360 = 1080
Share take up 1 * 320 = 320
1080 + 320 = 1400
1400 / 4 = 350
Ex rights = 350
Share Price Adjustment
Share Price Adjustment
3 for 5 Bonus Issue
Current Price £1,184
Existing 5 * 1,184 = 5,920
New issue 5,920 / 8 = 740
Current Price £1,184
New Price £740
Liquidity Ratio
Liquidity Ratio
Current Liabilities
Liquidity Ratio - Example
Liquidity Ratio
Current Liabilities
Assets £61,200, Stock £21,800 & Liabilities £27,600
£61,200 - £21,800 = £39,400
£39,400 / £27,600 = 1.43 (2 DP’s)
Liquidity Ratio = 1.43 (2 DP’s)
Price to Book Ratio
Price to Book Ratio
NAV Per Share
Price to Book Ratio - Example
Price to Book Ratio - Example
NAV Per Share
Share Price £410, NAV £180
410/180 = 2.28 (2 DP’s)
Net Asset Value (NAV)
Net Asset Value (NAV)
No of Ordinary Shares
Net Asset Value (NAV) - Example
Net Asset Value (NAV) - Example
No of Ordinary Shares
Net Assets £1,000, No of Ordinary Shares 20
£1,000 / 20 = £50
NAV = £50
Interest Cover
Interest Cover
Gross Interest Payable
Interest Cover - Example
Interest Cover - Example
Gross Interest Payable
Profit £27,000, Interest £3,400
£27,000 / £3,400 = 7.94
Interest Cover = 7.94 (2 DP’s)
Dividend Yield
Dividend Yield
Net Dividend Per Share
———————————– x 100
Share Price
Dividend Yield - Example
Dividend Yield - Example
Net Dividend Per Share
———————————– x 100
Share Price
Shares Price 342, Net Dividend 12
12 / 342 * 100 = 3.51% (2DP’s)
Payout Ratio
Payout Ratio
Net Dividend Per Share
———————————— X 100
Earnings Per Share
Payout Ratio - Example
Payout Ratio - Example
Net Dividend Per Share
———————————— X 100
Earnings Per Share
Earnings Per Share £20, Net Dividend Per Share £8
£8 / £20 = 0.4
0.4 * 100 = 40%
Payout Ratio = 40%
Dividend Cover
Dividend Cover
Total Earnings (Earnings Per Share) (Either or) ------------------------------------------------------- Total Dividend (Div Per Share) (Either or)
Dividend Cover - Example
Dividend Cover - Example
Total Earnings (Earnings Per Share) (EIther or) ------------------------------------------------------- Total Dividend (Div Per Share) (Either or)
Earnings Per Share £28, Dividend Per Share £12
£28 / £12 = 2.33
Dividend Cover 2.33
Price Earnings Growth (PEG)Ratio
Price Earnings Growth (PEG) Ratio
Earnings Growth
Price Earnings Growth (PEG)Ratio - Example
Price Earnings Growth (PEG) Ratio - Example
Earnings Growth
P/E 12, Earnings 6%
12 / 6 = 2
PEG Ratio = 2
Price Earnings (P/E) Ratio
Price Earnings (P/E) Ratio
Shares Price / Earnings
Ration between the share price and earnings per share
Price Earnings (P/E) Ratio - Example
Price Earnings (P/E) Ratio - Example
Share Price / Earning
Share Price £342, Earnings £28
342 / 28 = 12.21
P/E Ratio = 12.21
Earnings Per Share (EPS)
Earnings Per Share (EPS)
Earnings / Number of Ord Shares
Earnings Per Share (EPS) - Example
Earnings Per Share (EPS)
Earnings / Number of Ord Shares
Earnings £28,000,000, Ord Shares 100,000,000
£28,000,000 / 100,000,000 = 0.28
EPS = 0.28
Modified Duration
Modified Duration
1 + Gross Redemption Yield (GRY)
Modified duration is a measure of price sensitivity in response to interest rates.
The higher the duration the higher the volatiitly
Modified Duration - Example
Modified Duration - Example
1 + Gross Redemption Yield (GRY)
Macaulay Duration 4, GRY 5%
4 ------------------- = 3.81% (2 DP's) 1 + 5% = 1.05
A 1% change in Interest Rates would result in a 3.81% Change
Gross Redemption Yield (GRY)
Gross Redemption Yield (GRY)
Income + Loss or Gain
Gross Redemption Yield (GRY) - Example
Gross Redemption Yield (GRY) - Example
Income + Loss or Gain
5% ABC 2024
Purchase Price £124, Redemption Price (PAR) £100
Income = £100 * 5% = £5.00
£5.00 / £124 = 0.0403
0.0403 * 100 = 4.03% (2 DP’s)
Income = 4.03%
2024-2018 = 6 Years £124 - £100 = £24 £24 / 6 = £4 £4 / 124 = 0.0322 0.0322 * 100 = 3.23% (2 DP's) Loss/Gain = 3.23%
4.03% - 3.23% = 0.80%
Gross Redemption Yield = 0.80%
Holding Period Return
Holding Period Return
SV
V0
Holding Period Return - Example
Holding Period Return - Example
SV
V0
Money Weighted Return
Money Weighted Return
SV - (Top Up x N/12)
Money Weighted Return - Example
Money Weighted Return - Example
SV - (Top Up x N/12)
Return on Equity / Capital
Return on Equity / Capital
Capital
Profit
--------------------- x 100 Shareholder Funds + Liabilities
Equity
Earnings ---------------------- x 100 Shareholder Funds
Gearing (Debt / Equity)
Gearing (Debt / Equity)
Debt ------------------ X 100 Shareholder funds
Money Weighted Return (MWR) - Limitations
MWR is influenced by cash flows which could be outside the control of the fund manager
It does not identify whether the return is due to the ability of the manger or as a result of when additional funds are added
Information Ratio
The information ratio (IR) is a measure of portfolio returns above the returns of a benchmark, usually an index, to the volatility of those returns.
The information ratio (IR) measures a portfolio manager’s ability to generate excess returns relative to a benchmark, but it also attempts to identify the consistency of the investor.
The information ratio identifies how much a manager has exceeded the benchmark.
Higher information ratios indicate a desired level of consistency, whereas low information ratios indicate the opposite.
Many investors use the IR when selecting exchange-traded funds (ETFs) or mutual funds based on investor risk profiles.
Although compared funds may be different in nature, the IR standardizes the returns by dividing the difference by the standard deviation:
Information Ratio
Formula for Information Ratio (IR)
Sp-i
Where:
Rp = Return of the portfolio
Ri = Return of the index or benchmark
Sp-i = Tracking error (standard deviation of the difference between returns of the portfolio and the returns of the index)
Information Ratio vs. Sharpe Ratio
Information Ratio vs. Sharpe Ratio
Like the information ratio, the Sharpe ratio is an indicator of risk-adjusted returns. However, the Sharpe ratio is calculated as the difference between an asset’s return and the risk-free rate of return divided by the standard deviation of the asset’s returns.
The IR aims to measure the risk-adjusted return in relation to a benchmark, such as the Standard & Poor’s 500 Index (S&P 500), and it measures the consistency of an investment’s performance. However, the Sharpe ratio measures how much an investment portfolio outperformed the risk-free rate of return on a risk-adjusted basis.
Sharpe Ratio
The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk.
Subtracting the risk-free rate from the mean return, the performance associated with risk-taking activities can be isolated.
One intuition of this calculation is that a portfolio engaging in “zero risk” investment, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero.
Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.
Issues with Sharpe
It can be inaccurate when applied to portfolios or assets that do not have a normal distribution of expected returns. Many assets have a high degree of kurtosis (‘fat tails’) or negative skewness.
The Sharpe ratio also tends to fail when analyzing portfolios with significant non-linear risks, such as options or warrants. Alternative risk-adjusted return methodologies have emerged over the years, including the Sortino Ratio, Return Over Maximum Drawdown (RoMaD), and the Treynor Ratio.
Sharpe Ratio - Application
The Sharpe ratio is often used to compare the change in a portfolio’s overall risk-return characteristics when a new asset or asset class is added to it. For example, a portfolio manager is considering adding a hedge fund allocation to his existing 50/50 investment portfolio of stocks and bonds which has a Sharpe ratio of 0.67. If the new portfolio’s allocation is 40/40/20 stocks, bonds and a diversified hedge fund allocation (perhaps a fund of funds), the Sharpe ratio increases to 0.87. This indicates that although the hedge fund investment is risky as a standalone exposure, it actually improves the risk-return characteristic of the combined portfolio, and thus adds a diversification benefit. If the addition of the new investment lowered the Sharpe ratio, it should not be added to the portfolio.
Sharpe Ratio - Issues
The Sharpe ratio can also be “gamed” by hedge funds or portfolio managers seeking to boost their apparent risk-adjusted returns history. This can be done by:
Lengthening the measurement interval: This will result in a lower estimate of volatility. For example, the annualized standard deviation of daily returns is generally higher than that of weekly returns, which is, in turn, higher than that of monthly returns.
Compounding the monthly returns but calculating the standard deviation from the not compounded monthly returns.
Writing out-of-the-money puts and calls on a portfolio: This strategy can potentially increase return by collecting the option premium without paying off for several years. Strategies that involve taking on default risk, liquidity risk, or other forms of catastrophe risk have the same ability to report an upwardly biased Sharpe ratio. An example is the Sharpe ratios of market-neutral hedge funds before and after the 1998 liquidity crisis.)
Smoothing of returns: Using certain derivative structures, infrequent marking to market of illiquid assets, or using pricing models that understate monthly gains or losses can reduce reported volatility.
Eliminating extreme returns: Because such returns increase the reported standard deviation of a hedge fund, a manager may choose to attempt to eliminate the best and the worst monthly returns each year to reduce the standard deviation.
Sharpe Ratio
(Rp - Rf) / ?p
where:
Rp = the expected return on the investor's portfolio Rf = the risk-free rate of return ?p = the portfolio's standard deviation
