Introduction to Investment: formula sheet

Key formulas

Real return (approximate)

Real return ≈ Nominal return − Inflation rate

Shows why saving at a rate below inflation loses purchasing power. The exact form is (1 + nominal) ÷ (1 + inflation) − 1.

Total return from an investment

Total return = Income received + Capital gain (or − capital loss)

Return has two sources: income and change in price.

Simple percentage return

Return % = (Ending value − Beginning value + Income) ÷ Beginning value × 100

Use for a single period.

Core distinction

Saving = safety and access; Investment = risk for return over time; Speculation = short-term price bet

Remember as a ranking of risk and horizon.

Total return

Total return = Income + Capital gain

Income means interest, dividend or rent. Capital gain is selling price minus purchase price.

Percentage return

Return % = (Income + Capital gain) ÷ Purchase price × 100

Use the purchase price as the base, not the selling price.

Risk-return trade-off

Higher expected return ↔ higher risk

A general principle. Higher risk gives the possibility of higher return, not a guarantee.

Liquidity rule

More liquid = easier to convert to cash quickly at close to fair value

Liquidity risk is the chance you cannot do this when you need to.

Holding period return

HPR = (Ending value − Beginning value + Income) ÷ Beginning value

Income means dividends or interest received during the holding period. Multiply by 100 for a percentage.

Absolute return

Absolute return = (Ending value − Beginning value) ÷ Beginning value × 100

Ignores the time taken. Not suitable for comparing investments held for different periods.

Annualised return (more than one year)

Annualised return = (1 + HPR)^(1 ÷ n) − 1

n is the number of years. This is the compound annual rate (CAGR when there is no interim income).

Annualised return (less than one year)

Annualised return = (1 + HPR)^(365 ÷ days) − 1

A simple scaling, HPR × 365 ÷ days, is also used for rough work. Read the question for which is wanted.

Real return (exact)

Real return = (1 + nominal) ÷ (1 + inflation) − 1

This is the Fisher relation. Use it when the question asks for the exact real return.

Real return (approximate)

Real return ≈ Nominal return − Inflation rate

A close estimate when rates are low. The exact value is slightly lower than this difference when real return is positive.

Future value

FV = PV × (1 + r)^n

Compounding a present sum forward at rate r per period for n periods.

Present value

PV = FV ÷ (1 + r)^n

Discounting a future sum back to today at rate r.

Total risk

Total risk = Systematic risk + Unsystematic risk

Diversification reduces only the unsystematic part.

Interest rate and bond price

Market interest rate ↑ → bond price ↓; market interest rate ↓ → bond price ↑

Inverse relationship. Applies to existing fixed-coupon bonds.

Real return (approximate)

Real return ≈ Nominal return − Inflation rate

Shows the inflation risk effect. The exact form is (1 + nominal) ÷ (1 + inflation) − 1.

Reinvestment risk direction

Rates fall → reinvestment risk hurts; rates rise → reinvestment benefits

Opposite to the price effect on bonds.

General risk-return ladder

Cash and liquid funds < Debt < Gold and Real estate < Equity < Alternatives (typical expected risk)

A broad guide only. Actual risk depends on the specific instrument, such as a long-duration or low-rated bond.

Real return (approximate)

Real return ≈ Nominal return − Inflation

Shows why fixed returns below inflation lose purchasing power.

Total return of an asset

Total return = Income (dividend, interest, rent) + Capital gain

Gold gives only capital gain, unless held through an interest-bearing form such as sovereign gold bonds.

Liquidity ranking (typical)

Listed equity and ETFs, liquid funds > Bonds > Gold (physical) > Real estate and private alternatives

Real estate and private funds are the least liquid.

Product selection order

Goals → Time horizon → Risk profile → Asset allocation → Products

Products are chosen last. An answer that starts with a product is usually the trap.

Risk profile

Risk profile = Risk capacity + Risk tolerance (the lower one governs)

If capacity is low but tolerance is high, treat the client as low risk.

Horizon and risk guide

Short horizon → liquidity and capital stability; Long horizon → more room for growth assets

A general guide only. Risk capacity can override it.

Asset allocation

Sum of weights of all asset classes = 100%

Allocation is set at the portfolio level before individual products are picked.

Quick revision

• Investment means committing money now for expected future benefit, with some risk taken.
• Return, risk and liquidity are the three core features of any investment.
• Higher expected return generally comes with higher risk, but this is not guaranteed.
• Liquidity is how quickly an asset can be turned into cash without a large loss of value.
• Real return is nominal return adjusted for inflation; it shows the gain in purchasing power.
• Time value of money: a rupee today is worth more than a rupee later because it can earn a return.
• Compounding earns return on earlier returns; more frequent compounding gives a higher effective yield.
• Systematic risk affects the whole market and cannot be diversified away; unsystematic risk is specific and can be diversified.
• Inflation risk, interest rate risk, credit risk and liquidity risk are different; match each to its cause.
• Asset classes include equity, debt, real assets such as real estate and gold, and cash equivalents.
• Product choice should follow the client's goal, time horizon and risk appetite.
• Read every option fully; a 2-mark wrong answer costs more than a 1-mark one.

Common mistakes

• Treating saving and investment as the same thing. Fix: In exams, saving is about safety and access; investment accepts risk for higher expected return over a time horizon.
• Saying speculation is illegal or always bad. Fix: Speculation is a legitimate activity with high risk and a short horizon. The difference from investment is one of degree.
• Treating risk as only the chance of loss. Fix: In investing, risk is variability of outcomes around the expected return. It covers both better and worse outcomes.
• Believing higher risk always gives higher return. Fix: Higher risk offers the potential for higher return. It does not assure it. Choose options that say 'expected' or 'potential'.
• Leaving out dividend or interest when computing HPR. Fix: Always put income in the numerator along with the price gain.
• Dividing by the ending value instead of the beginning value. Fix: The base of a return is always what you invested at the start.
• Saying diversification removes all risk. Fix: Diversification removes only unsystematic risk. Systematic risk stays.
• Confusing interest rate risk with reinvestment risk. Fix: Interest rate risk is about price change of the bond. Reinvestment risk is about the rate earned on reinvested cash flows. Rising rates hurt the first; falling rates hurt the second.
• Treating debt as risk-free Fix: Remember credit, interest rate and inflation risks. Fixed promise is not the same as no risk.
• Saying gold gives regular income Fix: Physical gold gives only price gain. Interest comes only from instruments like sovereign gold bonds.

Exam tips

• Expect direct questions on the difference between saving, investment and speculation. Learn one keyword for each.
• Watch for options with words like 'guaranteed' or 'risk-free' in an investment context. They are usually wrong.
• In caselets, underline the client's horizon, need for income and risk tolerance before choosing the objective.
• Negative marking applies, so attempt only when you can eliminate at least one option with a clear reason.
• Expect definition MCQs. Learn one clean line for each feature and you can answer in seconds.
• Distrust options with 'guaranteed', 'always' or 'no risk'. They are usually the trap.
• Questions often ask you to rank products on liquidity, such as bank deposit, listed share, real estate. Think about how fast and at what cost each converts to cash.
• In caselets, link the client's need for cash soon to liquidity, and capital protection to safety, before choosing a product.