Formulas

Question 1

2.6: Foreign Exchange

FX forward rate calc

If not given payment conventions and number of days then assume d/b is:

1/12 for a monthly forward rate
1/4 for a 3 monthly forward rate
1/2 for a 6 monthly forward rate
1 for a 12- month forward rate

You need to make sure that you learn this for your exam.

Answer 1

FX forward rate =
spot rate x (1 +(quote currency interest rate x d/b)) /
(1 + (base currency interest rate x d/b))

Question 2

Annual Equivalent Rate

Used to compare accounts between different providers with different terms

this is for Interest calcs (for loans/savings)

Answer 2

AER = ((1 + r/n)^n - 1) x 100

r is the nominal rate expressed as a percentage
n is the number of interest payments in a year.

Question 3

future value

This lets us calculate how much a capital amount would be worth if it received a rate of interest at a certain rate over a certain period.

this is for Interest calcs (for loans/savings)

Answer 3

FV = CV (1 + r)^n

FV is future value
CV is current value
r is the nominal rate expressed as a percentage
n is the number of interest payments in a year.

Question 4

Real return

Used to calculate the effects of inflation on a cash investment

Answer 4

Real return = nominal return - inflation

Question 5

Convertible Corporate Bonds =

Conversion Value formula

Answer 5

Conversion Value = Conversion Ratio X Current Share Price

Conversion Ratio = Number of shares that £100 nominal can be converted into

Conversion Value = How much the conversion would be worth if the bond was converted into the current share price

Question 6

3.3.9: Convertible Bonds

How to calc where a convertible is tradable at a Premium or discount. (Used decide whether its worth buying the convertible or just buy shares directly)

VERY IMPORTANT TO LEARN

4.2: Convertible preference shares
LEARN THIS TOO

5.5.1: Traditional warrants
Learn this too

All of the above use a similar equation but each equation is slightly different

Answer 6

Conversion premium or discount =
((Market price of convertible / Conversion value) - 1) x 100

Conversion Value = Conversion Ratio X Current Share Price

Conversion Ratio = Number of shares that £100 nominal can be converted into (bonds)

Conversion Ratio = How many preference shares are needed to buy 1 ordinary share. (Convertible preference shares)

If percentage is positive = convertible trading at Premium, more expensive to buy shares through convertible, so better to buy the shares directly.

If percentage is negative = convertible trading at discount (discount to shares) meaning it is cheaper to buy the shares through the convertible, so better to buy convertible and then convert

Question 7

3.8 Bond pricing - go over again!!!

LOOK at annuity discount formula

Figure out how to find the Present Value of cashflows in a bond

Question 8

Calculating returns on a bond. This is used to compare returns of bonds. Useful where both bonds have different prices and coupon as it allows the person to figure out what is most cost effective

The Interest yield

Redemption yield

NOTE:

The Interest yield is also known as the income yield, current yield, running yield or the flat yield

The Interest yield looks at the income and the Redemption yield looks at the complete return.

Answer 8

Interest yield = (Coupon x 100)/Clean price

It is basically the annual income from the bond, expressed as a percentage of the price paid. DOES NOT TAKE INTO ACCOUNT CAPITAL GAIN/LOSS

Gross Redemption yield = Interest yield
+/- (gain or loss at maturity/number of years to maturity) / clean price

The redemption yield is a more accurate calculation of the yield on a bond, as it takes into account the running yield and the loss / gain that would be experienced at maturity.

Net redemption yield =
Same formula as above except multiply the interest yield part (the part of the formula that represents income ) by the persons tax free income tax rate to account for tax.
For a basic rate taxpayer multiply the coupon by 0.8
For a higher rate taxpayer multiply the coupon by 0.6
For an additional rate taxpayer multiply the coupon by 0.55

Question 9

5.5.1: Traditional warrants (Learn both calcs)

Warrant Gearing

Warrant Conversion

5.5.2: Covered warrants

Call warrant Payout

Put warrant payout

It’s important to get these right as there are frequent questions on them in the J12 exam.

Question 10

6.3: Additional Detail on the Pricing of Unit Trusts and OEICs

Dual-priced fund pricing calculations

Question 11

6.7: Closed-ended Funds / Investment Trust Companies

Calculating if Investment trusts shares are trading at discount or premium to NAV.

Positive = premium
Negative = discount

Question 12

6.7.1c: Gearing

investment TRUSTS

Gearing is expressed using the following formula:

Answer 12

Gearing is expressed using the following formula:

Total gross assets ÷ net assets x 100.

A figure of 100 means there is no gearing. 130 means the company is 30% geared.

Question 13

Chapter 7, 7.2

Depreciation of company assets. 2 equations to know.

The straight line method (Most common method used in the UK)

The reducing balance method. 

Answer 13

Straight line method =
(Original cost - disposal value)/useful economic life

The reducing balance method =
Uses a percentage depreciation value per year

Question 14

9.5: Bond Dealing

accrued interest for bonds. yOU NEED THIS WHEN TRYING TO CALCULATE DIRTY PRICE

tWO EQUATIONS. When a bond is bought cum dividend AND EX DIVIDNED

Answer 14

The settlement date will be the trade date + 1 day

The coupon is an annual rate, hence the need to divide by 2.

LOOK AT CALC

The UK settles on an actual / actual basis. This means that we need to calculate the actual days between the last coupon date and the settlement date, and the actual number of days in the coupon period. Some people find this very confusing but in fact as long as you know how many days there are in each month, then it is relatively simple. The simplest method is to draw out a timeline and then count the days!

IMPORTANT: UK bonds have an ex-dividend date (a date at which they move to an ex-dividend basis).

For UK bonds this is 7 business days before the coupon payment date.

Also Remember: Settlement date = T + 1day

Question 15

9.5: Bond Dealing

IMPORTANT: UK bonds have an ex-dividend date (a date at which they move to an ex-dividend basis).

Answer 15

For UK bonds this is 7 business days before the coupon payment date.

Also Remember: Settlement date = T + 1day

Question 16

RELOOK

Question 17

theoretical ex-bonus price

This calcs the new market price of a share after a company makes a bonus issue

Question 18

13.1.2b: CAPM formula

Answer 18

Expected risk adjusted return = (Risky x Beta) + risk free

Risky = market expectation - risk free

(ISOLATE RISKY ELEMENT because you are trying to establish a return that has been adjusted for the risks being taken.)

Whatever

Question 19

There are some limitations to CAPM:

Answer 19

Finding a risk-free rate is difficult. Common practice is to use 91-day Treasury Bills.

Choosing a market portfolio is sometimes easier said than done. The FTSE 100 index is commonly used in the UK, but assessing the return on an inappropriate market portfolio can lead to incorrect assumptions.

Beta must be assumed to be stable and is calculated on historic data, which always brings into question its future validity.

EXTRA:
Whilst the scale on the ruler may be questionable, as long as we use the same ruler for all investments, it can still help us compare one with another.

Others say CAPM is too linear in its approach as it only considers one factor in arriving at its conclusion.

It’s a simple relationship between risk and return by taking the securities systematic risk level and applying this to an average market return.

So, it’s all down to the security’s sensitivity to the market, as measured by its beta.

That’s one of the reasons why some people prefer ‘multi-factor’ models.

Question 20

13.1.3: Multi-factor models

Many believe that the relationship between risk and reward is far too complex to describe with a single market index, as other factors influence the returns gained. Therefore multi-factor models are used to look deeper than CAPM

For this exam, you need to recognise some of the alternatives.

Arbitrage pricing point
Fama & French model

Answer 20

Any multi-factor model attempts to describe returns affected by several factors. Choosing which ones can be tricky, but they share the same ideas:

Investors require extra returns for taking risk.
Investors appear to be predominantly concerned with the risk that cannot be eliminated by diversification.

Question 21

Efficent market = all information is available

Inefficient = Not all info is availabele

Question 22

13.1.4: Efficient Market Hypothesis (EMH)

Answer 22

In an open and efficient market (such as London) share prices react instantly to such information, good or bad so the price that is being paid in the market is always the fairest price / the ‘correct market price’ for the shares.

Therefore, it is not possible to outperform the market by picking undervalued shares.

if you believe the hypothesis, then you will believe that buying and selling shares is more about chance than skill so rather than bothering with expensive fund managers, investors would be better off with a tracker fund.

Question 23

13.1.4: Efficient Market Hypothesis (EMH)

There are three forms of EMH to be aware of

Weak Form Efficiency
Semi- Strong form efficiency
Strong form efficiency

Answer 23

Weak Form Efficiency = States that the current share price fully reflects all past price and trading information and that future prices cannot be predicted by analysing historical data.
So, any technical analysis of company information is meaningless as it has no bearing on the future.

Weak Form Efficiency = historical data cannot be predicted (technical analysis is useless)

Semi- Strong form efficiency =
This states that share prices adjust to all publicly-available information very rapidly and in an unbiased way. It perceives public information to be all past trading information, company accounts and other economic factors.
Again, analysis of the information looking for clues is meaningless

Strong form efficiency =
If you believe in strong form you would believe that the share price seen not only reflects public information but also all private information held by a firm’s directors.

EXTRA:
Whether you subscribe to the EMH theories or not, there have been some compelling studies that tend to support the weak form. That said, there are deficiencies present in the other forms that would lead us to believe that the markets are not as efficient as the theories suggest.

In less-efficient markets than ours, it may still be possible to sniff out a bargain, but with technological advances, this is becoming more difficult.

What it often comes down to is whether people believe in ‘active fund management’. It is true to say that few of these do regularly outperform the market and passive management is becoming more popular.

Question 24

13.1.5: Behavioural finance

Answer 24

This is the last area of investment theory that we will cover in this chapter. It concerns itself with how an investor’s decisions are affected by emotional and psychological factors.

Advocates of behavioural finance argue that, with the other models, an assumption is made that ‘individuals act rationally and consider all available information when making investment decisions’. They also argue that this assumption is missing the fact that our own beliefs limit and distort how we interpret information that we receive, which can lead to us reaching incorrect conclusions.

According to behavioural finance, emotional and psychological factors explain market anomalies that are not explained by traditional analysis.

Question 25

You can categorise psychological factors and behavioural biases in many ways, and they often overlap, but the main ones are:

Prospect theory / loss aversion
Regret
Overconfidence and over and under reaction

Answer 25

Prospect theory = states that people do not always behave rationally, particularly when they are facing a loss or a profit

People are often very protective of any gains they make but take more risks when faced with potential (real or paper) losses. There are many examples of people holding onto assets that have made a loss simply because they don’t want the loss to be ‘real’.

Regret =
As mentioned in loss aversion, investors tend to ‘hang on in there’ when faced with a loss, even when it would be prudent to cut their losses. It is almost a case of not wanting to admit a mistake has been made.

By not selling they can avoid regretting their purchase.

Overconfidence and over and under reaction =
Investors overestimate their own skills and underestimate the likelihood of bad outcomes.
Too much emphasis is placed on past performance and recent trends.

Question 26

13.2.1: Main investment risks
Capital risk
inflation risk
Interest or income risk
Currency Risk
Investment performance (shortfall risk)
Provider risk
Counterparty risk
Liquidity risk
Operational risk

Question 27

13.3: Risk Management (diversification and correlation)

Question 28

There are two main methods that an investor can use to construct a low-risk portfolio:

They could simply buy low risk assets, but this will almost certainly result in low returns.

They could buy risky assets, and then combine them in a way that collectively reduces the risk. This is achieved either by diversification and / or hedging the risk.

Question 29

Diversification is best achieved by combining assets that move in different directions. When done effectively, diversification can reduce non-systematic risk from a portfolio.

Correlation measures how the changes in prices or returns of two different assets are linked. It is derived using the covariance of the two assets.

Answer 29

Remember though, it can’t remove the market risk or systematic risk.

Question 30

Correlation measures how the changes in prices or returns of two different assets are linked. It is derived using the covariance of the two assets.

Covariance measures the direction of the relationship between the two assets; correlation measures the degree to which they are related and is expressed as a value between -1 and +1.

3 types of correlation:

Positive
Negative
No correlation

Answer 30

Positive correlation = move in line with eachother. A correlation of +1 between 2 assets means they will rise/fall in exactly the same way

Negative correlation = Opposite direction. Correlation of -1 means they are perfectly negatively correlated. If one falls, the other rises in exactly the same way

No correlation = No relationship. Both assets are affected by completely different things (this is hard to achieve in a globalised world)

More negatively correlated assets = more diversification, although finding negatively-correlated assets is quite difficult to achieve in reality.