Formulas

Question 1

Interest yield

Answer 1

Coupon or nominal yield divided by the clean price multiplied by 100

Coupon or nominal yield / clean price x100

this is essentially a percentage of the coupon in terms of the price paid

Chapter 1

Question 2

Redemption yield

Answer 2

Interest yield plus or minus the gain or loss to maturity divided by the number of years to maturity divided by the clean price multiplied by 100

interest yield +- ((gain to maturity/no years to maturity)/clean price) x 100

Chapter 1

Question 3

Earnings per share

Answer 3

Profit attributable to ordinary shareholders/number of ordinary shares in issue

Chapter 2

Question 4

Dividend yield

Answer 4

(Dividend per share/current share price) x 100

Chapter 2

Question 5

Dividend cover

Answer 5

Individual basis

• Earnings per share/dividend per share

Total profit basis

• profit attributable to ordinary shareholders/dividends paid to ordinary shareholders

Chapter 2

Question 6

Price earnings ratio

Answer 6

Current market price of share/earnings per share

Chapter 2

Question 7

Net asset value

Answer 7

Assets attributable to ordinary shareholders/number of ordinary shares in issue

Chapter 2

Question 8

Real rate of return

Answer 8

Interest rates minus inflation rates

Chapter 3

Question 9

Capital asset pricing model equation

Answer 9

This formula gives you the expected return on a risky investment

= Rf + Bi(Rm - Rf)

Rf - rate of return on risk free asset

Rm - expected return of market portfolio

Bi - measure of sensitivity of investments To movements in the overall market

(Rm - Rf) - market risk premium, The access return of the market over the risk free rate

Bi(Rm - Rf) - Risk premium of the risky investment

Chapter 4

Question 10

Two factor model

Answer 10

This also gives the expected return like the CAPM equation

=Rf + Bgdp + Bir

Risk free return plus risk premium based on the security sensitivity to all anticipated changes in GDP plus risk premium based on the securities sensitivity to an anticipated changes in interest rates

Chapter 4

Question 11

Compound interest and it’s derivative compound rate of return

Answer 11

Compound interest = Present value(1+interest rate)^no years

Compound rate of return = (future value/present value)^1/n - 1

We essentially want to reverse this to find r

Chapter 5

Question 12

Effective rate and how to use this to the the annual percentage rate AKA annual equivalent rate

Answer 12

(1 + interest rate/no years)^no years - 1

To get APR or AER you multiply effective rate by 100 as to depict it as a percentage to 2 decimal places

Chapter 5

Question 13

Present value

Answer 13

Future value / (1 + interest rate)^no years

Chapter 5

Question 14

Accumulation in discounting of regular savings

Answer 14

regular payment((1 + r)^n -1/r)

Chapter 5

Question 15

Real returns from nominal returns

Answer 15

Real return = nominal return - inflation

Chapter 5

Question 16

Diluted net asset value per share

Answer 16

Net assets + money subscribed by warrant holders/number of ordinary shares in issue + new shares issued to warrant holders

Chapter 7

Question 17

Gearing

Answer 17

(Total gross assets/net assets) x 100

Essentially

All capital/all capital - borrowed capital

Chapter 7

Question 18

Chargeable gain of an encashed offshore bond

Answer 18

(Number of days policyholder was resident in the UK/number of days the policy has run) X total gain

Essentially the time spent in the country as a fraction of time the bond ran multiplied by the total gain

Chapter 8

Question 19

Holding period return

Answer 19

(Income revived during period + value of portfolio at end of period - value of portfolio at start of period)/ value of portfolio at start of period

Chapter 11

Question 20

Money waited rate if return

Answer 20

= D + V1 - V0 - C / V0 + ((C x n)/12)

(Income revived during period + value at end of period - value at start or period - new money introduced during) / value at start of period + ((money introduced during period x n)/12)

Where n is the time remaining in the period as a fraction of the period I.E. added in 3rd month 9 months left so 9/12 is n

Chapter 11

Question 21

Time weighted rate of return

Answer 21

1 + TWR = (holding period return of each sub period + 1) all added together going on for n

1 + TWR = (1 + r) x ….. (1 +rn)

Chapter 11

Question 22

Sharpe ratio

Answer 22

return on investment – risk free return/standard deviation of the return on the investment

Chapter 11

Question 23

Jensen’s alpha

Answer 23

Actual portfolio return – (risk free rate of return + beta of the fund or portfolio (market return-risk free rate of return))

Jensen’s alpha is essentially the real return - CAPM, which is real return - estimated return

Chapter 11

Question 24

Information ratio

Answer 24

Portfolio or fund return – benchmark return/tracking error

Chapter 11

Question 25

Benchmark return

Answer 25

During asset allocation you select the fund this is then used as

Fund allocation x fund allocation actual performance = benchmark return

Do this as a decimal then convert back to %