# CT1 Financial Mathematics: Cheat sheet

Do you ever find yourself stressing over the idea of not knowing what exactly to prepare from CT1 Financial Mathematics for an interview? Does the idea of having to go through the whole study material just to prepare for an interview scare you?

Well, then you don’t have to worry anymore because you are at the right place. In this article I try to talk about the questions (with answers of course) one should be thorough with (from CT1) before going for an interview.

CT1 i.e. Financial Mathematics is all about the mathematics behind finance and how it works. Well since you are going through this article I am sure you already know what CT1 is about and so let’s get started with the questions:

• What is an annuity?
An annuity is a financial product that pays out a fixed stream of payments at fixed intervals, guaranteed for a fixed number of years.

• Describe forward and spot rate.
Forward rate tells us about current expectation of interest rate over future period that may start at a future time.
Spot rate tells us about the interest rate over a period that starts now.

• Define Arbitrage and state the ‘Law of One Price’
Arbitrage is a trading strategy that looks to make profits from small discrepancies in securities price. An arbitrage opportunity exists if either an investor can make a deal that would give him/her an immediate profit, with no risk of future loss or has zero initial cost, no risk of future loss, and a non-zero probability of future profit.
Law of One Price’ states that if we assume that there are no arbitrage opportunities in the market, then it follows that any two securities or combination of securities that gives exactly the same payouts must have the same price.

• Why do we assume that arbitrage opportunity does not exist?
The “No Arbitrage” assumption enables us to find the price of a complex instrument by replicating the payoffs i.e. we can construct a portfolio of assets with exactly the same payout as the investment we are interested in, then the price of the investment must be the same as that of the replicating portfolio.

• How is real rate of interest different from money rate of interest?
In simple terms, a real rate of interest is the rate that allows for inflation whereas money rates of interest ignore the effect of inflation. So in period of positive inflation, real rate of interest will be lower than the money rate of interest and in period of negative inflation, the real rate of interest will be higher than the money rate of interest.

• What is a zero coupon bond?
A zero coupon bond as the name implies is one that has no coupon payments i.e. there is no regular interest payments, instead the investor buys the bond at a discount price i.e. price lower than its face value and when the bond matures the investor receives the principal amount/face value associated with it.

• What is principle of consistency and where does it fail?
Principle of consistency states that in a consistent market the proceeds of an investment should not depend on the course of action taken by the investor i.e. A (t0, t2) = A(t0, t1)*A(t1,t2) where t0<=t1<=t2.Principle of consistency fails when the interest rate varies over the period or when the cash flows are deferred.

• Net Present Value Vs Internal Rate of Return – Which financial evaluation technique is better?
Net present value (NPV) is calculated as present value of cash inflows less present value of cash outflows. It gives the value of the project at the outset. Internal rate of return (IRR) is known as the discount rate at which NPV of a project is zero.The NPV method assumes that cash flows will be reinvested at the project’s current cost of capital whereas IRR assumes that the firm can reinvest cash flows at the project’s IRR. The assumption made while calculating NPV is more realistic because IRR may not reflect the true rate at which cash flows can be reinvested. NPV also has an advantage over IRR when a project has non-normal cash flows i.e. there is a large cash outflow during or at the end of the project which will lead to multiple IRRs.Both the tools are majorly used to evaluate the profits from the investments but the cons associated with IRR makes NPV a much better measure.

• Why do we need to immunize and how do we immunize?
We immunize our portfolio to protect our fund from any small changes in the interest rate. To immunize our portfolio, three conditions need to be met:

• Value of the assets at a given rate of interest should be equal to the value of the liabilities
• The volatility of asset and liability cash flow series is equal.

The convexity of asset cash flow series should be greater than that of the liability cash flow.

• Money Weighted Rate of Return vs Time Weighted Rate of Return- Which is a better measure of investment performance?   Money weighted rate of return (MWRR) is the yield earned over the investment period. Time weighted rate of return (TWRR) calculates the “growth factor” reflecting the changes in the value of the fund between the times of consecutive cash flows.MWRR is sensitive to the amount and timing of cash flows and it can be negative if there is one large cash flow generating negative return or it can be positive if the larger value cash flow is associated with high positive return.  TWRR eliminates the effects of cash flow amount and timing as this is beyond fund manager’s control and can therefore be more accurate when it comes to measuring investment performance.

• Talk about Derivatives and its types.
A derivative is a security with a price dependent on one or more underlying asset. Derivatives can be used for hedging or insuring against risk on an asset, betting on the future price of an asset or to avoid any exchange rate issues. The most common forms of derivatives are:

• FUTURES: A Future is a standardized, exchange tradable contract between two parties to trade a specified asset on a set date in the future at a price agreed upon today. This can be used to hedge against risk during a particular period of time.
• FORWARD CONTRACT: A forward contract is a customized, exchange tradable contract between two parties to trade a specified asset on a set date in the future at a price agreed upon today.
• OPTIONS: Options gives an investor the right, but not the obligation to buy or sell a specified asset on a specified future date. Here, the holder of the option is not obliged to trade.

SWAPS: A Swap is a contract between two parties under which they agree to exchange a series of payments according to a predetermined agreement. Swaps can be made using interest rate, currencies or commodities.

• Explain the difference between a call and put option.
A call option gives the holder the right, but not the obligation, to buy a specified asset on a set date in the future for a specified price. The potential gain in case of a call option is unlimited because the call generates money when the value of the underlying asset goes up.A put option gives the holder the right, but not the obligation, to sell a specified asset on a set date in the future for a specified price. The potential gain in case of a put option is limited because a put generates money when the value of securities is falling.

1. List the factors that help in determining the interest rate.
Factors that lead to changes in interest rates are:

• SUPPLY AND DEMAND: Interest rates are determined by market forces i.e. interaction between borrowers and lenders. So, if demand for money is higher than supply then it will lead to increase in interest rate and similarly if demand for money is lower than supply than the interest rate is expected to decrease.
• BASE RATE: In many countries there is a central bank that sets a base rate of interest which provides a reference point for other interest rates.
• INTEREST RATE IN OTHER COUNTRIES: As major investment institutions have the option of borrowing from abroad, so interest rate in a particular country is influenced by cost of borrowing in other countries.
• EXPECTED FUTURE INFLATION: The interest rate is expected to outstrip inflation.
• TAX RATES: If tax rates are high, interest rates may also be high because investors will require a certain level of return after tax.

RISK ASSOCIATED WITH INTEREST RATE: Rates of interest tend to increase as the term increases because of the risk of loss due to change in interest rates is greater for longer term investments.

2. Describe effective and nominal rate of interest?
Effective rates of interest are compound rates that have interest paid once per unit time either at the end of the period (effective interest) or at the beginning of the period (effective discount).Nominal rate of interest is paid more or less frequently than once per measurement period. A nominal rate of interest per period, payable pthly, i(p) is defined to be a rate of interest of i(p)/ p applied for each pth of the period.

i(p) is equivalent to pthly effective rate of interest of i(p)/ p.

3. Why does the Redington Immunization theory fail?
Redington Immunization theory fails when:

• The yield curve is not flat i.e. the change in the interest at all terms is not the same.

There are large changes in the interest rate. This theory relies on small changes in the rate of interest.

4. Discuss the theories of term structure of interest rate.
There are three essential theories that attempt to explain why yield curves are shaped the way they are:

• EXPECTATION THEORY: This theories states that the future movement in interest rate will determine the demand and supply of short and long term investments. An expectation of fall in interest rates will make short term investments less attractive and therefore the short term yield will increase and the long term will decrease.
• LIQUIDITY PREFERENCE: Longer dated bonds are more sensitive to interest rate movements than short dated bonds. So it is assumed that risk averse investors will require compensation for the greater risk of loss on longer bonds.

MARKET SEGMENTATION: This theory says that different investors adhere to specific maturity segments. This means that the term structure of interest rates is a reflection of prevailing investment policies.

Also don’t forget to go through all the formulas from CT1 before going for an interview.

Good Luck!