NISM RA study kit
Chapter 12 of 15

Fundamentals of risk and return

Worth 7 marks of 100Book pages 228 to 246, and 334 to 341About 75 minutes

Measure the return properly, name the risks you took to earn it, and judge the return per unit of risk. Then watch your own biases.

Chapter mapTwelve parts, plus the book's Annexure 3. 12.2 and 12.9 carry the numericals. Tap to jump.
12.1

Return on investment

An investor expects two things: a return, and, more importantly, the capital back. Safety of capital matters as much as return. Judge a return by its level, its volatility and its nature (periodic income or capital gain).

A return in rupees means little on its own; compare it with the capital that earned it.

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

Higher is better, and it is simple to use. But be careful with investments whose returns are not known in advance, such as equity and mutual funds: their ROI is an estimate built on past returns and assumptions.

12.2 Simple, annualised and compounded returns

A return measure should help investors judge whether the return is enough for their goals and risk, compare investments, and compare against a benchmark. Total return = periodic income (interest, dividend, rent) + change in value, whether realised or not. Gold and other commodities give no periodic income at all.

One investment, three return figuresThe book's example: 150 shares bought at Rs 25, sold at Rs 30, Rs 1 dividend per share, Rs 20 brokerage each way

Total cost

150 × 25 + 20 = Rs 3,770

Total returns

Sale 150 × 30 − 20 = 4,480. Dividend 150. Total Rs 4,630

Simple (holding period) return

4,630 ÷ 3,770 − 1 = 23%

If held 15 months

Simple annualised return

(23% ÷ 15) × 12 = 18.4%

Divide by months (or days) held, multiply by 12 (or 365).

If held 5 years

CAGR

(4,630 ÷ 3,770)1/5 − 1 = 4.2%

Counts compounding.

CAGR = (End value ÷ Beginning value)1/n − 1, where n = years held
  • The simple return ignores time: 23% over one year is not the same as 23% over five.
  • Simple annualising ignores compounding. Most interest calculations assume compound interest.
  • CAGR assumes periodic returns are reinvested. It is the smoothed rate at which the investment grew. Actual yearly returns differ, and that difference reflects the risk.
  • CAGR is the accepted standard measure of return, except for periods under one year.
  • With several cash flows on different dates, use Excel's XIRR. The book's example: buy at Rs 150 on 31 July 2011; dividends of Rs 5, 6 and 4 each October; sell at Rs 165 on 15 January 2014. CAGR = 8.06%.
Try it: simple, annualised and CAGRDefaults are the book's example held for 5 years (60 months)
simple (holding period) return
simple annualised
CAGR
12.3

Risks in investments

Risk is the volatility and uncertainty of returns and, at the extreme, loss of capital. An investment is also risky if actual returns differ from expected ones. A bank fixed deposit is low risk; equity is risky because dividends are uncertain and values swing. Higher return comes only with willingness to take higher risk. Investors should know which risks they face: a retired investor may accept low returns but not loss of capital.

Ten risks, as described in the book
RiskWhat it isBook's example or note
Inflation (purchasing power)Money received is worth less after inflationHighest in fixed-return instruments: an 8% bond with 7% inflation earns 1% real. Lower for equity, as profits rise with prices. Venezuela 2018: inflation 65,370%; bonds became almost worthless; the Caracas index rose over 1,000 times
Interest rateBond prices fall when rates rise and rise when rates fallAlso hits equity: higher cost of capital lowers present value, borrowing and profits
BusinessRisk in operations; measured as the standard deviation of EBIT or EBITDAIncludes commodity, operations, competition, supply chain and currency risk. Reduced by holding varied businesses
MarketLoss from adverse price moves in a traded assetAffects equity, bonds, gold, real estate. Deposits and small savings have none, but also do not appreciate
Credit (default)Issuer may not pay interest or principalA sovereign has no default risk on local-currency debt (it can tax or print). Measured by credit ratings: AAA and A1 highest, D is default. Reduced by diversifying
LiquidityCannot sell when wanted, or only below value, or at high costIndian corporate bonds, property and art; lock-ins. Book: a Sovereign Gold Bond order book on 17 July 2020 had a bid-ask gap above Rs 80 (about 2%)
CallA bond is called before maturityMost common when rates are falling: issuers replace high-coupon bonds. Goes with reinvestment risk
ReinvestmentCoupons may have to be reinvested at a lower rateRates rise: risk falls. Rates fall: risk rises. A cumulative option avoids it (but a bond may then swing more in price)
PoliticalUnfavourable government action: nationalisation, tax or licensing changesAlmost all businesses are exposed
CountrySocio-economic-political-cultural risks of a country; it may not honour its commitmentsA country default affects all securities issued there
Asha's fixed deposit pays her Rs 5,000 a month, enough for groceries. Prices rise 10%, and groceries now cost Rs 5,500. Her deposit is perfectly safe, yet she is poorer. That is inflation risk.
"Liquidity" has three meanings in the book: a company's ability to meet short-term obligations; an asset's ease of conversion into cash (shares and bonds easy, gold and real estate harder); and a market's depth of ready buyers and sellers. Check which one a question means.

Systematic and unsystematic risk

Can diversification remove it?The book's classification
Systematic (undiversifiable)

Felt across investments: government policy, external factors, wars, natural calamities.

Market, inflation, exchange rate, interest rate, reinvestment risk.

Unsystematic (diversifiable)

Specific to one security or a small group. Reduced by adding other assets.

Credit, business, liquidity risk.

  • Ajay buys shares of an infrastructure company. A change in the government's push for infrastructure hits all infra companies: unsystematic, reduced by investing in other sectors. Rising rates or a recession hit everyone: systematic, seen as market risk.
  • Ashima buys bonds. She cuts credit risk by holding more highly rated bonds, but if rates rise, all her bonds fall: interest rate risk, common to all debt.
12.4

Measuring risk

Risk is the variability of possible outcomes, both up and down, though we usually mean the downside. The book separates risk from uncertainty: when we know nothing about a cause (like a tsunami or COVID before they happened), it is uncertainty; once research explains the cause, it becomes a measurable risk. Risk is "known uncertainty".

Three ways to measure risk
1. Statistical

Standard deviation

Variability of returns around the mean. For a sample: s = √[Σ(X − mean)² ÷ (n − 1)].

2. Sensitivity

Elasticity measures

  • Beta: stock returns versus index returns; market (systematic) risk
  • Modified duration: bond price versus interest rates; interest rate risk
  • Delta: option price versus the underlying's price; market risk
3. Loss

Value at Risk (VaR)

Maximum loss over a period at a given confidence level. VaR (1%) of 12%: 99% confident the loss will not exceed 12%; a 1% chance it will. Confidence level = 1 − significance level.

12.5 Beta

Beta measures systematic risk relative to the market index: the risk that cannot be diversified away. It is used in CAPM (Chapter 10).

Beta = 1

Moves with the market. Market +10%: stock +10%.

Beta below 1

Less volatile than the market.

Beta above 1

More volatile. Beta 1.2, market +15%: stock +18%.

Not everyone trusts betaValue investor Seth Klarman, quoted in the book, calls it "preposterous" that one number from past price moves could describe a security's risk. Beta ignores business fundamentals and the price paid (IBM at $50 is less risky than at $100), and assumes upside and downside are equal. Past volatility does not reliably predict future performance.
12.6

Sensitivity analysis

A valuation model is only as good as its inputs. Identify the critical variables and see how the value changes when one variable changes and all others stay constant. That is sensitivity analysis. Example: in a DCF, run the valuation at several discount rates and tabulate the results. Scenario analysis instead takes a best case, a worst case and the most likely case.

12.7 Margin of safety

Popularised by Benjamin Graham, "the father of value investing", and followers such as Warren Buffett. Margin of safety is the gap between value and price when a security is bought well below its intrinsic value. The bigger the gap, the bigger the margin.

  • It allows investing with minimal downside risk, but does not guarantee success.
  • It gives a cushion against errors in the analyst's valuation, which is subjective anyway.
  • There is no universal standard for how wide it should be; each investor sets their own.
An engineer rates a bridge for 30 tonnes but lets only 10-tonne trucks cross. The gap covers the mistakes nobody knows they made.

12.8 Equity returns versus bond returns

How bond and equity returns differ
BondsEquity
Main source of returnCoupon income, plus some gain when rates fallAppreciation in value; dividend is a small part
AssurancePre-defined coupon; may be securedNo assurance of dividend or appreciation
Risk and returnLower risk, so lower returnHigher risk
Primary riskDefault risk: higher credit risk means higher interestCompany performance and the economy

Buffett, as quoted in the book: compare the returns on bonds and stocks when deploying capital. If stocks offer more, buy stocks; if bonds offer more, buy bonds. In distress, rates fall sharply and equities may be "dirt cheap" even on dividend yield.

12.9

Risk-adjusted returns

A high-risk strategy usually earns more in the long run but swings more. So compare portfolios on return per unit of risk. For all three measures below, higher is better.

Jensen's alpha, Sharpe, Treynor
MeasureFormulaRisk usedSuits (as per the book)
Jensen's alphaPortfolio return − [Rf + β × market risk premium]Beta (systematic). Excess over the CAPM return 
Sharpe ratio(Portfolio return − Rf) ÷ Standard deviationTotal risk (standard deviation)Investors with much of their wealth in one investment, not adequately diversified
Treynor ratio(Portfolio return − Rf) ÷ BetaBeta (systematic)Investors who have adequately diversified across asset classes
Try it: risk-adjusted returnsAll rates in % a year
Sharpe ratio
Treynor ratio
Jensen's alpha

Sharpe divides by standard deviation; Treynor divides by beta. Jensen's alpha is a difference (return minus the CAPM return), not a ratio. The book says Jensen's alpha "factors the systematic risk using equity beta".
12.10

Behavioural biases

Classical finance assumes people are rational. In practice, emotion and psychology drive decisions. Benjamin Graham, in "The Intelligent Investor", said markets are more psychological and less logical. Behavioural finance combines psychology with economics to explain irrational financial decisions. Simon Savage of GLG Partners, quoted in the book: "We were all born to be bad fund managers because of inbuilt behavioural biases."

Eight biases to watch
Loss aversion

Strongly preferring to avoid losses over making gains. The pain of a loss is about twice as strong as the pleasure of an equal gain. Leads to inaction: holding losers, avoiding equity when volatility is in the news.

Confirmation (my-side) bias

Seeking or reading information so it confirms what you already believe. A trader whose reason for buying fails invents a new reason to hold.

Ownership bias (endowment effect)

Valuing what you own more than others would. You hold positions you would not buy at today's price.

Gambler's fallacy

Predicting random events from the past: believing something that happened often will now happen less, or the reverse, to "balance" things.

Winner's curse

Winning a competitive bid by overpaying. A behavioural win, a financial loss.

Herd mentality

Following others in the belief they know more. Leads to bubbles and crashes; small investors enter when markets are overheated. Keynes: "It is better for reputations to fail conventionally than to succeed unconventionally."

Anchoring

Relying too much on the first piece of information. Waiting for a "right price" to sell that is no longer realistic, and ignoring new information.

Projection bias

Projecting the recent past into the distant future, ignoring the more distant past.

12.11 Wisdom from investment gurus

Markets move in bull and bear cycles. Great investors teach discipline through both.

  • Bull market: buyers pay higher and higher prices. Businesses are growing fast with strong demand, or there is just a change in perception or too much liquidity. It can overdo it: prices go past intrinsic value, firms borrow for expansion on rosy forecasts, and input, labour and interest costs rise near the peak. Unrealistic prices tend to correct with a crash.
  • Bear market: prices fall. Businesses face lower demand, higher costs and less access to capital; some fail. Sellers quit in despair. When prices fall well below value, buyers return, central banks cut rates, and the next bull cycle slowly begins.
Graham's Mr. MarketYou own a business with a partner, Mr. Market, who offers every day to buy your share or sell you his, at prices swayed by his moods. Do not let his emotions drive yours. Use his mispricing as an opportunity.
Quotes the book collects
Benjamin Graham

"In the short run, market is a voting machine but in the long run, it is a weighing machine."

"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks."

Warren Buffett

"Rule No.1 is never lose money. Rule No.2 is never forget rule number one."

John Templeton

"Invest at the point of maximum pessimism."

Peter Lynch

"Go for a business that any idiot can run, because sooner or later, any idiot is probably going to run it."

David Dreman

"Psychology is probably the most important factor in the market, and one that is least understood."

Walter Schloss

"If you can't find good value investing positions, park your money in cash."

Charlie Munger

"Understanding how to be a good investor makes you a better business manager and vice versa."

12.12 Measuring liquidity of shares

Stock exchanges exist to provide liquidity, but not every share is liquid: liquidity needs many buyers and sellers.

Stock turnover ratio

Shares traded in a period (usually a year) ÷ free float shares outstanding.

Free float: shares held by non-promoter shareholders.

Traded value turnover ratio

Traded value of shares ÷ market capitalisation.

A3

Annexure 3: Lessons from history

The book ends with real cases from market history. Its point: life is too short to learn only from your own mistakes, so learn from others'. It quotes Mark Twain: "We learn from the past that we don't learn from the past."

Case 1: the Barings collapse

Nick Leeson headed derivatives trading at Barings Futures Singapore, a subsidiary of Barings Plc, London. He was a star trader and a favourite of top management. He ran both the front office (trading) and the back office (checking and reporting).

How Barings fellAnnexure 3, Case 1

The bet

Sold many straddles (a call and a put sold together) on Nikkei 225 index futures, on SGX-DT in Singapore and the Osaka Securities Exchange. A straddle loses if the market moves sharply either way. It was a bet that Japan's market would stay stable.

The shock

A violent earthquake hit Kobe. The Nikkei fell and the put side of his straddles lost money.

Doubling down

Instead of cutting the loss, he bought huge long Nikkei futures on both exchanges to hold the index up. He told London it was arbitrage between the two exchanges, and told each exchange he had opposite positions on the other.

The collapse

One trader could not turn the market. It kept falling, and Barings failed on both the futures and the straddles. The exchanges stayed safe because they had collected margins.

Five lessons from Barings

  1. One trader cannot move the market. Work with the market and manage the position: here, cut the loss on the short puts.
  2. Set clear position limits for each trader, by product, market or total exposure, and tell every trader.
  3. Monitor the limits closely. Leeson broke his limits and sent false reports, which went unnoticed because he ran the back office himself. Keep front and back office under different people. Systems should block a trader at the limit.
  4. Exchanges should share information on large positions. The two exchanges competed for Nikkei business and never cross-checked. Sharing also deters manipulation across two exchanges.
  5. Big institutions are as prone to risk as individuals. Collect margins from everyone, on time. SEBI applies margins to all categories of participants, including institutions.

Lessons 1 to 3 are for trading firms, 4 for exchanges, and 5 is the one SEBI has acted on in India.

The book's verdict"Barings' failure was not the derivatives failure, it was management's failure." The Board of Banking Supervision blamed poor operational controls (operational risk), not derivatives. Afterwards, firms worldwide separated front and back office, exchanges began sharing information, and all positions came to be margined.

Case 2: the credit event of 2008

How the 2008 crisis built upAnnexure 3, Case 2. The book's account, from 2003 to 2004 onwards
Banks

Lent to less creditworthy borrowers and loosened loan to value (for example from 80:20 to 85:15) to earn higher margins (NIMs). They assumed ever-rising house prices would cover any default: a view on real estate, which is not a banker's job.

Selling the loans

To lend more, banks sold long-dated mortgages to investors at lower yields, booked the profit up front and earned bigger bonuses. They stopped caring about credit quality as long as someone bought: moral hazard. Lending became a fee business.

Home buyers

Got almost 100% financing, so they treated a house like a call option: if prices rose, sell and keep the profit; if prices fell, hand the keys to the bank.

Investors and raters

Funds bought mortgage-backed securities and passed them on, like passing the pillow. Rating agencies gave them top grades (AAA kind) based on history and the hard assets behind them. Many credit derivatives were written on them too.

When prices began to fall, defaults rose and it came down like a pack of cards. The last holders were left with securities worth a couple of cents to the dollar.

Lessons from 2008

  • Banks are leveraged, so they must stay disciplined. Their business is lending, not betting on asset prices. Risk management is the heart of banking; never dilute it to win business.
  • Investors should do their own due diligence, not just rely on rating agencies, and keep asking: "What could go wrong here?"
  • History matters, but decisions cannot rest only on historical data. Rating agencies leaned on past mortgage data. The book notes no rating agency ever stood up to take responsibility.
  • Respect the limits of what you understand. Nassim Taleb: "Black Swan events pose significant risk in this integrated world." Risk management should come first.

Frauds the book lists

Warren Buffett: "People with pen do much bigger thefts than the people with guns."

Disgraced companies and fund managersFacts as stated in the book
WhoWhat happenedOutcome in the book
EnronPower trading company. Massive accounting fraud wiped out $78 billion of market valueBankrupt in 2001. Former President Jeff Skilling: 24 years in prison
WorldComTelecom giant. Top management manipulated the financials; once had over $100 billion in assetsFraud-induced bankruptcy in 2002. Former CEO Bernard Ebbers: 25 years
Satyam ComputersPromoter Ramalinga Raju confessed in 2009 to inflating cash and bank balances by about Rs 5,000 crore, after a failed bid to buy Maytas, another promoter-owned companyJailed on fraud charges. Satyam was later acquired by Tech Mahindra
Bernard MadoffNew York money manager. $65 billion Ponzi scheme, the largest financial fraud in US history, exposed in December 2008Sentenced in June 2009 to 150 years
Michael MilkenDrexel's "Junk Bond King" of the mid-1980s. Brought down by insider trading10 years in prison; $600 million fine
Raj RajaratnamCo-founded hedge fund Galleon Group in 1997. Arrested in October 2009 for insider tradingSentenced in October 2011 to 11 years and a $10 million fine

All exam traps in this chapter

  1. ROI = net profit ÷ investment × 100. Safety of capital matters as much as return.
  2. Simple (holding period) return ignores time; simple annualising ignores compounding.
  3. Simple annualised = HPR ÷ months × 12.
  4. CAGR = (end ÷ beginning)1/n − 1. The standard measure, except for periods under one year.
  5. Multiple cash flows on different dates: use XIRR.
  6. Inflation risk is highest for fixed-return instruments and lower for equity.
  7. Bond prices move opposite to interest rates.
  8. Business risk is measured as the standard deviation of EBIT or EBITDA.
  9. Deposits and small savings have no market risk.
  10. A sovereign has no default risk on local-currency borrowing.
  11. Credit ratings: AAA and A1 highest, D default. SEBI standardised the symbols.
  12. Call risk is most prevalent when rates are falling.
  13. Reinvestment risk rises when rates fall and falls when rates rise.
  14. Systematic: market, inflation, exchange rate, interest rate, reinvestment. Unsystematic: credit, business, liquidity.
  15. Beta measures market risk; modified duration, interest rate risk; delta, option sensitivity.
  16. VaR (1%) of 12%: 99% confident the loss will not exceed 12%.
  17. Beta above 1: more volatile than the market. Beta 1.2 and market +15% gives +18%.
  18. Sensitivity analysis changes one variable at a time; scenario analysis uses best, worst and most likely cases.
  19. Margin of safety: Benjamin Graham; no universal standard; no guarantee.
  20. Jensen's alpha = Rp − [Rf + β × MRP]. Sharpe uses SD; Treynor uses beta.
  21. Sharpe suits undiversified investors; Treynor suits well-diversified ones.
  22. Loss aversion: losses hurt about twice as much as equal gains please.
  23. Ownership bias is also called the endowment effect. Confirmation bias is also called my-side bias.
  24. Graham: short run a voting machine, long run a weighing machine.
  25. Stock turnover ratio uses free float shares; traded value turnover uses market cap.
  26. Barings: "not the derivatives failure, it was management's failure". The root cause was operational risk: one person ran front and back office.
  27. A short straddle loses if the market moves sharply either way. Leeson's was a bet on a stable Nikkei.
  28. 2008: banks diluted loan to value, sold loans on (moral hazard), and investors leaned on AAA ratings without their own due diligence.

For the group discussion

  1. Your fixed deposit earns 7% and inflation is 6%. Your friend's equity fund fell 10% this year. Who took more risk?
  2. Which bias do you recognise most in your own investing? Give a real example.
  3. Klarman says beta is a poor measure of risk. Do you agree? What would you use instead?
  4. Two funds both returned 18%. What else would you ask before choosing one?
  5. How wide a margin of safety would you want before buying a share? Why that number?
  6. Barings and 2008 were both called failures of management, not of the products. Do you agree?