Formulas/calcs Flashcards
Interest yield on bonds
Also known as flat yield or running yield.
Calculation of the income return the investor gets. Doesn’t take into account whether if held to redemption, there will be a loss or gain.
Interest yield = coupon (as a %) / clean price
x 100
AER
Annual equivalent rate
Deposit takers must display this way to allow savers to compare rates. There are many different ways the rate can be advertised, referred to as the nominal rate.
2 a/cs, same nominal rate but interest paid at different frequency will = different AER
AER = (1+r/n)n -1
r = rate of interest as decimal (divide % by 100)
n = number of interest paument periods, I.e. quarterly = 4 monthly = 12.
Conversion premium/discount on convertible bonds
What is it & the formula.
Give right to convert the bond into a pre-defined number of ordinary shares, on a set date or between a range of dates, before bond maturity.
Formula looks at whether it is better to buy the convertible bond or the shares directly.
market price of convertible stock ÷
conversion ration x market price of ordinary stock
-1
x100
So, £100 nominal stock can be converted into 25 shares.
Bond currently trading at 110p per stock & shared currently priced at 400p
((100 x 1.10)÷ (25 x 4.00)) -1 x100
(110÷100) -1 x100
1.1 -1 x100
0.1 x100
10%
Shows buying the convertible bond is 10% more expensive than buying the shares directly.
Redemption yields on bonds
Takes into account the gain or loss if held to redemption, not just the interest earnt.
flat yield + (((par value - market value) / number of yrs to redemption)
÷
market price)
x100
Volatility on a bond - calc called Macaulay Duration or just Duration
The longer period to redemption, the more volatile the bond.
The lower the coupon, the more volatile the bond.
Formula used to assess how sensitive to the market one bond is compared to another.
Works out the present value of the cash flow (money received in income/ withdrawals) I.e. what it’s worth in today’s terms.
By adding them all together you get the current price of the bond.
You then x by the number of the year & total it up.
Finally divide the total present value by the total present value x years figure
Return on property/ initial yield
Initial yield used by property investors to compare investment opportunities.
Inaccurate to compare with other investments as doesn’t allow for rental growth a lease provides through rent reviews.
= Actual rental income
÷
Price of the property
x100
If there is an expense provided, take this off the actual rental income before dividing by the price of the property.
Return on a treasury bill
You’ll hopefully have an average price per £100 nominal.
Divide the amount you have available to invest by £100 & then times by the average price to get how much is needed to be invest.
Then take the amount being invested off the amount you had available to invest.
Divide that answer by the amount being invested to get the % return.
Modified duration on a bond
Modified duration measures how sensitive a bond is to changes in interest rates.
Duration / (1+ gross redemption yield)
Gives you the % price change for every 1% change in yields.
If yields rise, the price of the bond should fall.
Rights issue to raise new funds & theoretical ex-rights price
Rights issues give the right to subscribe for new shares at a lower price.
E.g. Current market price is £3.50 per share but the rights issue gives the right, for every 3 ordinary shares held you can buy one new ordinary share for £2.
Before the rights issue 3 shares at £3.50 = £10.50
After rights issue = the 4 shares are valued at £12.50 (3x£3.50 + 1x£2) so the theoretical ex-rights price will fall to £12.50÷4 = £3.13
Share bonus issue & the impact on share price
Example: company could give 1 new shares for every two held (1:2).
The overall value of investors holdings will stay the same but the value is spread across more shares and so the individual share price drops.
Held 2 shares priced at £2 per share = £4
Now holds 3 shares so £4 ÷ 3 = share price drops to £1.33 per share.
Share splits & effect on share price
Example: A 5:1 split means every 1 share is split into 5.
Share price = £10
Before split - 100 shares valued at £1,000
After split - 500 shares values at £,1000 so £1,000 / 500 = £2
Hedging your position in relation to the FTSE
The number of contracts requires to hedge a portfolio = hedging ratio.
The future is priced in index points with a tick value of £10.
If the index future is £7500, each contract is valued at £7500 x £10 = £75,000.
To find out how many contract you need to sell you divide the value of the portfolio you want to hedge by the value of the futures contract.
£1mil portfolio ÷ £75,000 = 13.33
Round up to whole number. 14 contracts need to be sold.
If the FTSE & futures price then falls you can calculate the protection of the futures contract.
Portfolio value x the drop in the FTSE (worked out by dividing the new FTSE value by the old)
Take the answer from the portfolio value to get the loss.
Then compare it to the impact of the future.
Work out the drop in the futures contract price (minus one from the other).
x £10 per index point.
x the number of contracts sold
You can see if the amount from the future covered the drop in the portfolio.
Capital asset pricing model (CAMP) & Beta - what is it?
Says because non-systemic risk can be eliminated by diversification, it is not rewarded. It is the sensitivity of the security to the market that is the appropriate measure of risk.
The sensitivity is expressed in terms of its beta.
The marker has a beta of 1.
Beta = 1 - will move with the market.
Beta = more than 1 - more volatile than the market, will go up and down by more. Aggressive securities.
Beta = less than 1 - more stable than the market, will move up and down less. Defensive securities.
CAPM gives the theoretical expected return as a combination of the return on a risk free asset and compensation for holding a risky asset (risk premium).
Provides the relationship between a security’s systemic risk and it’s expected return. High betas can expect high returns in a rising market.
CAPM formula
E(Ri) = Rf + Bi (Rm - Rf)
E(Ri) = Expected return on risky investment
Rf = return of risk-free asset
Bi = Beta (actually a weird B)
Rm = expected return of market portfolio
Holding period return on investment
Used to compare returns on different investments in a consistent manner. Shows total return, including income and capital gains over the period.
R =
D + V1 - V0
÷
V0
Remember to take into account the number of shares. Multiply the values by the number of shares.
x by 100 to express answer as a %
D = income
V1 = selling price
V0 = acquisition price
