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AF 4 - Alan > Calculations > Flashcards

Calculations Flashcards

1
Q

CAPM Calculation

A

E (R) = Rf + β (E(Rm) - Rf)

Rf = Risk Free Return

β = Beta

E(Rm) Expected Market Return

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2
Q

C.A.P.M

A

Links the expected return of an investment to its Beta

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3
Q

Effective Rate of Interest (A.E.R.)

A

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):
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4
Q

Effective Rate of Interest (A.E.R) - Example

A

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%
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5
Q

Time Value of Money - Accumulation of Money

A

Amount (1 + r)n

r = Interest rate
n = Time Period * this is to the power
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6
Q

Annualised rate of return

A

PV (1 + r)n = FV

PV = Present Value
r = rate of return
n = number of time periods * this is to the power
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7
Q

Annualised rate of return - Example

A

PV (1 + r)n = FV

PV = £3,000 
FV = £3,383 in 4 years time

r = £3,383 / £3,000 = 1.1276

  1. 1276 √4 = 1.0304
  2. 0304 - 1 = 0.0304
  3. 0304 = 100 = 3.04%
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8
Q

Working Capital

A

Working Capital = Current Assets / Current Liabilities

Links back to changes in Assets and Liabilities
Good measure of resilience and efficicency

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9
Q

Operating Profit Margin

A

Operating Profit Margin = Operating Income (EBIT) / Sales Revenue * 100

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10
Q

Operating Profit Margin - Example

A

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)

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11
Q

Working Capital Ratio

A

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)

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12
Q

Increase in Revenue

A

Increase in Revenue

(Current Year - Previous Year)/Previous Year * 100

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13
Q

Increase in Revenue - Example

A

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%

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14
Q

Return on Equity (ROE)

A

Profit / Total Equity

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15
Q

Return on Capital Employed (ROCE)

A

ROCE

Operating Profit x 100%) / (Capital Employed = Equity + Long term borrowing

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16
Q

ROCE - Notes

A

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.

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17
Q

TWR Time Weighted Returns

A

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

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18
Q

TWR Time Weighted Returns - example

A

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

  1. 055 * 1.005 = 1.0603
  2. 0603 - 1 = 0.0603
  3. 0603 * 100 = 6.03% (2 DP’s)
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19
Q

Dividend Yield

A

Dividend Yield

Dividend Per Share / Market Price of Share

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20
Q

Dividend Yield Notes

A 
High Yield 
Little expectation of growth
Losses / Insolvency
Negative Capital Growth
Special Dividend
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21
Q

Dividend Cover

A

Dividend Cover

Post Tax Profit / Dividend Paid (to ordinary shareholders)

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22
Q

Rights Issue - Rights Premium

A

Rights Issue - Rights Premium

Ex Rights Price - Issue Price

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23
Q

Rights Issue - Rights Premium - Example

A

Rights Issue - Rights Premium

Ex Rights Price - Issue Price

Ex Rights Price £350
Issue Price £320

£350 - £320 = £30

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24
Q

Rights Issue

A

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

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25
Q

Share Price Adjustment

A

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

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26
Q

Liquidity Ratio

A

Liquidity Ratio

Current Liabilities

27
Q

Liquidity Ratio - Example

A

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)

28
Q

Price to Book Ratio

A

Price to Book Ratio

NAV Per Share

29
Q

Price to Book Ratio - Example

A

Price to Book Ratio - Example

NAV Per Share

Share Price £410, NAV £180

410/180 = 2.28 (2 DP’s)

30
Q

Net Asset Value (NAV)

A

Net Asset Value (NAV)

No of Ordinary Shares

31
Q

Net Asset Value (NAV) - Example

A

Net Asset Value (NAV) - Example

No of Ordinary Shares

Net Assets £1,000, No of Ordinary Shares 20

£1,000 / 20 = £50

NAV = £50

32
Q

Interest Cover

A

Interest Cover

Gross Interest Payable

33
Q

Interest Cover - Example

A

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)

34
Q

Dividend Yield

A

Dividend Yield

Net Dividend Per Share
———————————– x 100
Share Price

35
Q

Dividend Yield - Example

A

Dividend Yield - Example

Net Dividend Per Share
———————————– x 100
Share Price

Shares Price 342, Net Dividend 12

12 / 342 * 100 = 3.51% (2DP’s)

36
Q

Payout Ratio

A

Payout Ratio

Net Dividend Per Share
———————————— X 100
Earnings Per Share

37
Q

Payout Ratio - Example

A

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%

38
Q

Dividend Cover

A

Dividend Cover

Total Earnings (Earnings Per Share)                     (Either or)
-------------------------------------------------------
Total Dividend (Div Per Share)                             (Either or)
39
Q

Dividend Cover - Example

A

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

40
Q

Price Earnings Growth (PEG)Ratio

A

Price Earnings Growth (PEG) Ratio

Earnings Growth

41
Q

Price Earnings Growth (PEG)Ratio - Example

A

Price Earnings Growth (PEG) Ratio - Example

Earnings Growth

P/E 12, Earnings 6%

12 / 6 = 2

PEG Ratio = 2

42
Q

Price Earnings (P/E) Ratio

A

Price Earnings (P/E) Ratio

Shares Price / Earnings

Ration between the share price and earnings per share

43
Q

Price Earnings (P/E) Ratio - Example

A

Price Earnings (P/E) Ratio - Example

Share Price / Earning

Share Price £342, Earnings £28

342 / 28 = 12.21

P/E Ratio = 12.21

44
Q

Earnings Per Share (EPS)

A

Earnings Per Share (EPS)

Earnings / Number of Ord Shares

45
Q

Earnings Per Share (EPS) - Example

A

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

46
Q

Modified Duration

A

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

47
Q

Modified Duration - Example

A

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

48
Q

Gross Redemption Yield (GRY)

A

Gross Redemption Yield (GRY)

Income + Loss or Gain

49
Q

Gross Redemption Yield (GRY) - Example

A

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%

50
Q

Holding Period Return

A

Holding Period Return

      SV
      V0
51
Q

Holding Period Return - Example

A

Holding Period Return - Example

      SV
      V0
52
Q

Money Weighted Return

A

Money Weighted Return

  SV - (Top Up x N/12)
53
Q

Money Weighted Return - Example

A

Money Weighted Return - Example

  SV - (Top Up x N/12)
54
Q

Return on Equity / Capital

A

Return on Equity / Capital

Capital

            Profit
        ---------------------                    x 100 Shareholder Funds + Liabilities

Equity

  Earnings     ----------------------             x 100 Shareholder Funds
55
Q

Gearing (Debt / Equity)

A

Gearing (Debt / Equity)

      Debt 
 ------------------         X 100 Shareholder funds
56
Q

Money Weighted Return (MWR) - Limitations

A

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

57
Q

Information Ratio

A

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:

58
Q

Information Ratio

A

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)

59
Q

Information Ratio vs. Sharpe Ratio

A

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.

60
Q

Sharpe Ratio

A

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.

61
Q

Issues with Sharpe

A

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.

62
Q

Sharpe Ratio - Application

A

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.

63
Q

Sharpe Ratio - Issues

A

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.

64
Q

Sharpe Ratio

A

(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

AF 4 - Alan (5 decks)

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