Fundamentals of Risk and Return — the ground floor

An investor wants two things back

Put money into anything and you want two things: a return, and — the workbook says this is the more important of the two — the capital back. It is blunt about it: "the preservation or safety of the capital invested is as important a parameter in evaluating an investment as is the return that it is expected to provide." A return you cannot keep is not a return.

And a return has to be judged on three things, not one:

• the level of the return — how much
• the volatility in the return — how reliable
• the nature of the return — periodic income, or capital appreciation

Rupees are not a return

Suppose someone tells you they made ₹40,000 last year. Good? You cannot say. On ₹1 lakh it is excellent; on ₹40 lakh it is poor. The workbook puts it exactly this way: "The return that an investment generates in money terms is not a correct representation of its level of return. The return must be seen in conjunction with the capital invested to earn it."

Return on investment (%) = (Net profit ÷ Investment) × 100

Higher ROI is better, and as a decision tool it is simple. One caution the exam likes: be careful with ROI for investments where returns are not known in advance — equity and mutual funds. There you are working from past returns and assumptions, not from a promise.

Total return = income received + change in value

Returns arrive in two shapes.

Periodic payouts — interest, dividends, rent. Known in advance (interest on a fixed income instrument) or varying (equity dividends), and in gold and other commodities absent altogether. High, low or zero, this is always a positive cash flow.

Change in value — positive or negative. A gain adds to the return; a loss eats into whatever periodic income there was.

Two points that get tested: a price increase counts as return whether or not you have sold — the workbook says it is "used in the calculation of the RoI, whether it is realized or not" — and together, income plus value change form the total return.

The workbook's own share example

An investor buys 150 shares at ₹25, pays ₹20 brokerage; receives ₹1 per share as dividend; sells at ₹30, pays ₹20 brokerage again.

Notice where the two brokerages go. Buy-side brokerage is added to cost; sell-side brokerage is subtracted from proceeds. Both reduce your return, but they sit on opposite sides of the fraction.

This 23% is the holding period return, also called the simple return — and it has a hole in it: it says nothing about how long the money was tied up.

Annualised return: putting every investment on the same clock

The workbook: "A 23% return earned over a one year is not the same as a 23% return earned over a longer or shorter investment period." So convert the holding period return to a uniform period — typically one year. The method is deliberately simple arithmetic:

Annualised return = Holding period return ÷ number of months × 12 (or ÷ number of days × 365)

If that 23% was earned over 15 months:

(23% ÷ 15) × 12 = 18.4%

CAGR: the same job, done properly

The simple annualised figure has its own hole: it does not consider the compounding effect. Time value of money says money received earlier is worth more than money received later, and as a matter of convention most interest rate calculations assume compound interest, not simple interest.

Compounded Annual Growth Rate (CAGR) fixes this. It assumes the periodic returns are re-invested to earn returns, and it is the rate of return at which the original investment grows to the final value.

CAGR = (End Value ÷ Beginning Value)^(1 ÷ n) − 1, where n is the holding period in years.

Take the same investment, but held 5 years instead:

3,770 × (1 + r)^5 = 4,630 (1 + r)^5 = 4,630 ÷ 3,770 = 1.23 r = 1.23^(0.2) − 1 = 0.04227

CAGR = 4.2%. The same 23% that looked like 18.4% on a 15-month view is worth only 4.2% a year when it took five years to earn.

Two footnotes the workbook adds. It ignored the timing of the dividend — carried forward with interest to the sale date, the CAGR would have been higher by some basis points. And CAGR is the accepted standard measure of return on investment in financial markets — except for periods of less than one year.

The sentence to memorise: CAGR is a smoothened rate. The actual return in each year of the holding period may be different from the CAGR.

When cash flows are messy: XIRR

Direct CAGR only works with one amount in and one amount out. Put dividends in the middle at irregular dates and the formula breaks. The workbook's example: buy on 31 Jul 2011 for ₹150; dividends of ₹5 on 31 Oct 2011, ₹6 on 31 Oct 2012, ₹4 on 31 Oct 2013; sell on 15 Jan 2014 for ₹165.

"This problem cannot be solved using the direct CAGR formula." Use the XIRR function in Excel — dates in one column, matching cash flows in the next. The answer is 8.06%. The test centre gives you Excel or LibreOffice Calc; XIRR is not a trick, it is an instruction.

What risk actually is

The workbook gives a working definition worth quoting: "Risk is the variability in the values of any expected outcomes."

Three consequences follow, and each shows up in questions.

• Risk is both positive and negative. Variability upward is still variability. We discuss only downside risk because that is what hurts.
• An investment is risky if actual returns differ from expected returns — even pleasantly.
• "Risk is known uncertainty." Before the tsunami, before COVID, nobody understood the phenomenon — that was uncertainty. Research identified the causal factors, and only then did it become tsunami risk or COVID risk. Research converts uncertainty into risk, and only then can risk be measured.

The ten risks, in the workbook's order

A few details inside that table are exam-grade on their own.

Inflation risk. Asha lives on ₹5,000 a month of fixed deposit interest, which just covers her provisions. Inflation rises 10% and she needs ₹5,500 for the same basket. Her capital never fell; her purchasing power did. On a bond: an 8% coupon against 7% inflation gives a real return of just 1%, and at 9% inflation the real return turns negative — with no default at all.

Equity handles inflation better: if prices rise, businesses raise selling prices, nominal profits rise, and stock prices tend to follow. The workbook's illustration is Venezuela, where inflation peaked at 65,370% in 2018 (prices roughly 654 times higher). Bond investors were nearly wiped out; the Caracas Stock Exchange index rose over 1000 times in the same year.

Interest rate risk. A 5-year bond, face ₹100, coupon 8%. RBI cuts rates; new bonds of similar rating are issued at 7.5%. Everyone wants the old 8% bond, so its price rises until its IRR is about 7.5%. Reverse it: rates rise, new bonds pay 9%, holders dump the old bond and its price falls until its IRR matches the market. Summed up:

• If interest rates fall, or are expected to fall, bond prices go up.
• If interest rates rise, or are expected to rise, bond prices decline.

Equity is not exempt. In theory a higher cost of capital lowers the present value of cash flows. In practice, dearer borrowing means less capex, hence less revenue and profit, while higher interest costs cut profits directly. Either way the cash flows to equity investors fall, demand falls, and prices fall.

Credit risk. A sovereign government has no default risk on its local currency borrowings — it can tax, or print. All other borrowings have credit risk. It is measured through credit ratings, whose symbols SEBI has standardised: AAA and A1 are the highest credit worthiness, D represents default. Ratings are not static. A lower rating means higher perceived default risk, so investors demand a higher interest rate — a higher borrowing cost for the issuer.

Liquidity risk. Liquidity has three different meanings and you must know which one is being discussed: of a company (its ability to meet immediate short-term obligations — a capacity); of an asset (how easily it converts to cash — shares and bonds yes, gold and real estate relatively illiquid); of a market (ready buyers and sellers who can transact significant quantity without much price impact).

The workbook's illustration: the order book of the Sovereign Gold Bond maturing December 2025 at the end of 17 July 2020. The gap between best bid and best ask was over ₹80 — about 2% — with very little quantity on offer.

Call risk and reinvestment risk travel together. Call risk is most prevalent when interest rates are falling, because a company saving money will redeem a high-coupon bond and reissue at a lower rate. For reinvestment risk the direction is the opposite of what most people guess: if interest rates rise, reinvestment risk reduces or is eliminated; if interest rates fall, reinvestment risk increases.

Choosing the cumulative option available in most debt investments protects against reinvestment risk — though in a marketable security that may mean higher price volatility.

Systematic and unsystematic risk

This is the single most-tested idea in the chapter.

Systematic risk is felt across investment categories. It comes from factors affecting the economy or markets as a whole — government policy changes, external factors, wars, natural calamities. It is also called undiversifiable risk, because diversification cannot remove it.

Unsystematic risk is specific to individual securities or a small class of investments. It is also called diversifiable risk, because adding other assets to the portfolio removes it.

Memorise the two lists exactly as the workbook gives them:

The workbook's own illustrations. Ajay buys shares of an infrastructure company. A change in the government's push towards infrastructure hits all infrastructure companies — unique to that sector, so unsystematic, and Ajay escapes it by investing in other sectors. But rising interest rates or a recession hit everything, and no other business can help him diversify that. Ashima buys bonds: she reduces credit risk by holding more highly rated bonds, but if rates rise every bond she holds falls — interest rate risk is common to all debt investments.

Measuring risk — three families

(i) Statistical measure. The most common definition of investment risk is variability of returns around the mean returns, calculated as standard deviation. The workbook gives the sample version, s = √[ Σ(X − X̄)² ÷ (n − 1) ], where X̄ is the average rate of return and n the number of observations. Note the n − 1 — that is what makes it a sample estimate.

(ii) Measures of sensitivity, all elasticity coefficients — percentage change in one variable for a percentage change in the risk-causing variable. Beta: sensitivity of a stock's returns to index returns, assessing systematic risk. Modified duration: sensitivity of a bond's price to small changes in interest rates — interest rate risk. Delta: sensitivity of an option's price to a change in the underlying — market risk.

(iii) Measure of loss. Value at Risk (VaR) measures the maximum loss one may suffer, during a given period, at a particular level of confidence. If VaR (1%) of a portfolio is 12%, then with 99% confidence the loss will not exceed 12% — equivalently there is a 1% probability the loss exceeds 12%. And confidence level = 1 − significance level.

Beta, in detail

Beta measures systematic risk relative to the volatility of the market, represented by a market index. It is a proxy of risk that cannot be diversified away.

The workbook then does something unusual for an exam text: it prints a long objection to beta from Seth Klarman of the Baupost Group, who calls it "preposterous that a single number reflecting past price fluctuations could be thought to completely describe the risk in a security." Klarman's charges — beta ignores business fundamentals, ignores the price level, ignores the influence investors can exert, and assumes upside and downside are equal — end with the line worth carrying: past price volatility does not reliably predict future performance, or even future volatility.

Know beta. Know also that knowing beta is not the same as knowing risk.

Sensitivity analysis and margin of safety

Sensitivity analysis is what you do when a valuation model depends on assumptions. "The output from the model is only as good or reliable as the quality of the variables that have been plugged in to it." Identify the critical variables, change one at a time keeping all others constant, and tabulate how the valuation moves. In a DCF the obvious candidate is the discounting rate. Alongside it runs scenario analysis — best case, worst case and most likely case.

Margin of safety was popularised by Benjamin Graham, "the father of value investing", and his followers, most notably Warren Buffett. It is the difference between value and price, when securities are bought at a price significantly below their intrinsic value. The bigger the gap with value above price, the bigger the margin.

Two qualifications the exam loves. It allows an investment to be made with minimal downside risk, but does not guarantee a successful investment — it is room for error, a cushion against the analyst's judgement, because intrinsic value is highly subjective. And there is no universal standard for how wide the margin should be; each investor must come up with his or her own number.

Equity returns versus bond returns

The workbook attributes a decision rule to Warren Buffett: always compare the returns on bonds and stocks when deploying capital. If the rate of return on stocks is greater than on bonds, buy stocks; if the rate of return on bonds is greater, deploy into bonds. It adds that during economic distress rates are pushed sharply down and equities may be available at very cheap valuations, even on a dividend yield basis.

Risk-adjusted returns

The premise: a high-risk strategy is likely to produce higher returns in the long run, but will also be more volatile. So comparing absolute returns of two portfolios is not appropriate. Three measures fix it.

Jensen's Alpha = Return on portfolio − (Risk free rate + β × market risk premium) — it factors the systematic risk using equity beta, the bracket being the CAPM expected return.

Sharpe ratio = (Return on portfolio − Risk free rate) ÷ Standard deviation — the risk premium per unit of standard deviation. Appropriate for investors who have put a significant portion of their wealth in a particular investment and have not adequately diversified.

Treynor ratio = (Return on portfolio − Risk free rate) ÷ Beta — the risk premium per unit of beta. Appropriate for investors who have adequately diversified their wealth into multiple asset classes.

For all three, higher is better. The logic behind the Sharpe/Treynor split is worth holding on to: if you are undiversified your unsystematic risk is still live and standard deviation captures total risk, so Sharpe; if you are properly diversified only systematic risk remains, which beta measures, so Treynor.

Behavioural biases

Conventional theory assumes rational wealth-maximising participants. Behavioural finance exists because they are not. Benjamin Graham, in The Intelligent Investor, said markets are more psychological and less logical. Simon Savage of GLG Partners put it more sharply: "We were all born to be bad fund managers because of inbuilt behavioural biases."

On herd mentality the workbook quotes John Maynard Keynes: "It is better for reputations to fail conventionally than to succeed unconventionally."

Bull markets, bear markets, and Mr. Market

A bull market is when buyers pay higher and higher prices on optimism — or on nothing more than a change in perception or excessive liquidity in the system. Exuberance overdoes itself: prices move beyond intrinsic values, businesses overarch and borrow on optimistic forecasts, input and interest costs climb near the peak, and the expansion corrects itself with a crash. In the bear market that follows, demand falls, costs rise, capital gets harder to raise, and sellers quit in despair — until prices fall below intrinsic value, value buyers step in and central bankers cut rates.

Benjamin Graham's Mr. Market is the allegory to remember. An investor puts 1,000 dollars into a business with a partner, Mr. Market, who values the firm daily and offers to buy him out or sell him more. Sometimes the assessment reflects real business events; often it reflects his own emotions. Graham's proposition: do not let Mr. Market's emotions drive your emotions — look for opportunities to exploit when he misprices the business.

Also printed: Graham's "In the short run, market is a voting machine but in the long run, it is a weighing machine", John Templeton's "Invest at the point of maximum pessimism", and Warren Buffett's "Rule No.1 is never lose money. Rule No.2 is never forget rule number one."

Measuring the liquidity of equity shares

Stock exchanges exist to provide liquidity, but not all shares are liquid — that needs a large number of buyers and sellers. Two ratios:

• Stock turnover ratio = number of shares traded in a period ÷ number of outstanding free float shares. Usually measured over one year. Free float means shares held by non-promoter group shareholders.
• Traded value turnover ratio = traded value of the shares ÷ market capitalisation of the company.

Beyond the book: two well-documented Indian episodes make these risks concrete. The IL&FS default in 2018 was credit risk arriving suddenly in instruments that had carried top ratings, and it showed how fast a rating can move. Franklin Templeton's winding up of six debt schemes in April 2020 was liquidity risk in its purest form — the underlying corporate bonds were sound on paper but could not be sold at a fair price when redemptions arrived. Both are unsystematic risks in theory, and very painful when concentrated.