By Deepak Jha, founder of BullWiser. Last updated 19 September 2026. Part of the NISM XV numerical practice hub.
NISM Series XV tests calculations mainly in Chapters 8, 9, 10, 12 and 15, which together carry 51 of the 100 marks. This page covers eight numerical topics. For each one you get the formula, questions from the free test solved step by step, extra worked examples and the mistakes that cost marks.
The solved questions are from BullWiser's first free 20-question numerical test (Free Test 1). They are BullWiser's own questions, not NISM's. Want to test yourself first? Take the free test, then come back to check your working.
Under the CAPM, the required return on a stock is ke = rf + β × (Rm − rf). The term (Rm − rf) is the market risk premium. A stock with a beta of 1 earns the market return and a stock with a beta of 0 earns the risk-free rate. The result is the discount rate in the dividend discount model and the equity cost in WACC.
Syllabus location: Chapter 10: Valuation Principles. This chapter carries 12 marks in the 100-mark exam.
| Measure | Formula | Note |
|---|---|---|
| CAPM required return | ke = rf + β × (Rm − rf) | Rm is the expected market return, not the premium. |
| Market risk premium | Rm − rf | Extra return the market pays over the risk-free rate. |
| WACC | E/V × ke + D/V × kd × (1 − tax rate) | Use after-tax cost of debt and market-value weights. |
| Gordon growth value | P0 = D0 × (1 + g) ÷ (ke − g) | ke from CAPM is the discount rate. Needs ke > g. |
The risk-free rate is 6%, the expected market return is 11% and a stock has a beta of 1.25. What is its required return under the CAPM?
Formula: Required return = rf + β × (Rm − rf).
Working: 6% + 1.25 × (11% − 6%) = 6% + 6.25% = 12.25%.
Common traps: The market premium is Rm − rf = 5%, not Rm. Using 11% as the premium gives 19.75%. Forgetting to add rf gives 6.25%.
rf = 7%, expected market return = 12.5%, beta = 0.8.
Premium = 12.5 − 7 = 5.5%. ke = 7 + 0.8 × 5.5 = 7 + 4.4 = 11.4%.
rf = 6.5%, market risk premium = 6%, beta = 1.5.
ke = 6.5 + 1.5 × 6 = 15.5%. Do not subtract rf again: the 6% is already the premium.
Equity is 60% of capital with ke = 14%. Debt is 40% with a pre-tax cost of 10%. The tax rate is 30%.
After-tax kd = 10 × (1 − 0.30) = 7%. WACC = 0.60 × 14 + 0.40 × 7 = 8.4 + 2.8 = 11.2%.
D0 = Rs 4, growth = 6%, ke = 12%.
D1 = 4 × 1.06 = 4.24. Value = 4.24 ÷ (0.12 − 0.06) = Rs 70.67.
P/E = price ÷ EPS. P/B = price ÷ book value per share. PEG = P/E ÷ expected growth rate (in percent). EV/Sales = enterprise value ÷ sales. To turn an enterprise-value multiple into a share price, subtract net debt and divide by the number of shares. Margin of safety = (intrinsic value − price) ÷ intrinsic value.
Syllabus location: Chapters 10 and 3: Valuation Principles and Terminology. Chapter 10 carries 12 marks and Chapter 3 carries 2 marks.
| Measure | Formula | Note |
|---|---|---|
| P/E ratio | Price ÷ EPS | Implied price = P/E × EPS. |
| Book value per share | (Share capital + reserves) ÷ number of shares | Number of shares = share capital ÷ face value. |
| P/B ratio | Price ÷ book value per share | |
| PEG ratio | P/E ÷ growth rate in percent | Growth of 20% enters as 20, not 0.20. |
| Enterprise value | Market cap + debt + preference + minority interest − cash | Net debt = debt − cash. |
| Value per share from an EV multiple | (Multiple × metric − net debt) ÷ shares | Metric is sales, EBITDA or similar. Also deduct preference capital and minority interest if the question gives them. |
| Margin of safety | (Intrinsic value − price) ÷ intrinsic value | Denominator is intrinsic value. |
A company has equity share capital of Rs. 60 crore (face value Rs. 10 per share) and reserves of Rs. 260 crore. Its share trades at Rs. 210. What is the price-to-book value (P/B) ratio?
Formula: Book value per share = (share capital + reserves) ÷ number of shares. P/B = price ÷ book value per share.
Working: Shares = 60 ÷ 10 = 6 crore. Net worth = 60 + 260 = Rs 320 crore. Book value per share = 320 ÷ 6 = Rs 53.33. P/B = 210 ÷ 53.33 = 3.94 times.
Common traps: Using reserves alone (260 ÷ 6 = 43.33) gives 4.85 times. Dividing the price by the face value gives 21.00.
A company's trailing EPS is Rs. 12 and stocks in its sector trade at a P/E of 22 times. At the sector P/E, what is the implied share price?
Formula: Implied price = P/E × EPS.
Working: 22 × 12 = Rs 264.
Common traps: Rs 0.55 comes from dividing instead of multiplying (12 ÷ 22). P/E tells you how many rupees the market pays per rupee of earnings, so price is always the larger number.
A stock trades at a P/E of 18 times and its earnings are expected to grow at 20% a year. What is its PEG ratio?
Formula: PEG = P/E ÷ expected annual earnings growth (growth entered as a whole number of percent).
Working: 18 ÷ 20 = 0.90.
Common traps: 1.11 inverts the ratio and 360 multiplies the two numbers. A PEG below 1 is often read as cheap relative to growth, but that is a rule of thumb, not a guarantee.
A company has sales of Rs. 800 crore and net debt of Rs. 400 crore, with 10 crore shares. Similar companies trade at an EV/Sales of 1.5 times. What is the implied value per share?
Formula: EV = multiple × sales. Equity value = EV − net debt. Value per share = equity value ÷ shares.
Working: EV = 1.5 × 800 = 1,200. Equity value = 1,200 − 400 = 800. Per share = 800 ÷ 10 = Rs 80.
Common traps: Skipping the net-debt step gives Rs 120. Adding net debt instead of subtracting it gives Rs 160.
An analyst estimates the intrinsic value of a stock at Rs. 600 and it trades at Rs. 420. What is the margin of safety, measured as (intrinsic value - price)/intrinsic value?
Formula: Margin of safety = (intrinsic value − price) ÷ intrinsic value.
Working: (600 − 420) ÷ 600 = 180 ÷ 600 = 30.0%.
Common traps: Dividing by the price instead of intrinsic value gives 42.9%. 70.0% is price ÷ intrinsic value, which is not the margin.
EPS = Rs 8.50 and the sector P/E is 18.
Price = 18 × 8.50 = Rs 153.
Share capital Rs 40 crore (face value Rs 10), reserves Rs 360 crore, price Rs 250.
Shares = 40 ÷ 10 = 4 crore. Net worth = 400. Book value per share = 400 ÷ 4 = Rs 100. P/B = 250 ÷ 100 = 2.5 times.
P/E = 30 and expected growth = 25%.
PEG = 30 ÷ 25 = 1.2. A PEG near 1 is often read as fair value for the growth, and below 1 as cheap. That is a rule of thumb.
EBITDA = Rs 250 crore, peer multiple = 10, net debt = Rs 300 crore, shares = 10 crore.
EV = 2,500. Equity value = 2,500 − 300 = 2,200. Per share = Rs 220.
Sales = Rs 1,200 crore, EV/Sales = 0.8, net debt = Rs 200 crore, shares = 20 crore.
EV = 960. Equity value = 760. Per share = Rs 38.
Intrinsic value Rs 250, price Rs 200.
(250 − 200) ÷ 250 = 20%. Dividing by the price would give 25%, which is the wrong denominator.
Interest coverage = EBIT ÷ interest expense. ROE = PAT ÷ average shareholders' equity. Total asset turnover = revenue ÷ total assets. Free cash flow = cash flow from operations − capital expenditure. Read the question for what it already includes: EBIT is after depreciation, and dividends never reduce free cash flow.
Syllabus location: Chapter 8: Company Analysis (Financial Analysis). This chapter carries 12 marks in the 100-mark exam.
| Measure | Formula | Note |
|---|---|---|
| Interest coverage | EBIT ÷ interest expense | EBIT = PBT + interest. |
| ROE | PAT ÷ average equity | Average equity = (opening + closing) ÷ 2. Use closing only if the question says so. |
| DuPont ROE | Net margin × asset turnover × equity multiplier | Equity multiplier = total assets ÷ equity. |
| Total asset turnover | Revenue ÷ total assets | Fixed asset turnover uses net fixed assets. |
| Free cash flow | Cash flow from operations − capex | Dividends and buybacks are uses of FCF. |
| Current ratio | Current assets ÷ current liabilities | Quick ratio excludes inventory. |
| Debt-equity ratio | Total debt ÷ shareholders' equity |
A company reports EBIT of Rs. 240 crore, depreciation of Rs. 20 crore (already deducted in arriving at EBIT) and interest expense of Rs. 90 crore. What is its interest coverage ratio (EBIT basis)?
Formula: Interest coverage = EBIT ÷ interest expense.
Working: 240 ÷ 90 = 2.67 times.
Common traps: Depreciation is already deducted in reaching EBIT, so adding it back (260 ÷ 90 = 2.89) is wrong for an EBIT-based ratio. 0.375 is the ratio upside down.
A company earned a PAT of Rs. 90 crore. Shareholders' equity was Rs. 700 crore at the start and Rs. 740 crore at the end of the year. What is its ROE on average equity?
Formula: ROE = PAT ÷ average shareholders' equity, where average equity = (opening + closing) ÷ 2.
Working: Average equity = (700 + 740) ÷ 2 = 720. ROE = 90 ÷ 720 = 12.50%.
Common traps: Opening equity gives 12.86% and closing equity gives 12.16%. If the question says average, use the average.
A company generated cash flow from operations of Rs. 640 crore, spent Rs. 120 crore on capital expenditure and paid dividends of Rs. 40 crore. What is its free cash flow (CFO - capex)?
Formula: Free cash flow = cash flow from operations − capital expenditure.
Working: 640 − 120 = Rs 520 crore.
Common traps: Dividends are paid out of free cash flow, they are not deducted in computing it. Subtracting them too (640 − 120 − 40 = 480) is wrong.
A company has revenue of Rs. 2400 crore, total assets of Rs. 1200 crore and net fixed assets of Rs. 300 crore. What is its total asset turnover?
Formula: Total asset turnover = revenue ÷ total assets. Fixed asset turnover = revenue ÷ net fixed assets.
Working: 2,400 ÷ 1,200 = 2.00 times.
Common traps: Dividing by net fixed assets gives fixed asset turnover (2,400 ÷ 300 = 8.00 times). Check which asset base the question names. 0.50 is the ratio inverted.
PBT = Rs 150 crore, interest = Rs 30 crore.
EBIT = 150 + 30 = 180. Coverage = 180 ÷ 30 = 6.0 times. PBT is after interest, so it must be added back.
PAT = Rs 60 crore, opening equity 500, closing equity 560.
Average = 530. ROE = 60 ÷ 530 = 11.32%.
Net margin 8%, asset turnover 1.5 times, equity multiplier 2.0.
ROE = 8% × 1.5 × 2.0 = 24%.
Revenue Rs 1,800 crore, net fixed assets Rs 600 crore, total assets Rs 900 crore.
Fixed asset turnover = 1,800 ÷ 600 = 3.0 times. Total asset turnover = 1,800 ÷ 900 = 2.0 times.
CFO Rs 500 crore, capex Rs 180 crore, dividends Rs 60 crore.
FCF = 500 − 180 = Rs 320 crore. The dividend is paid out of FCF and is ignored.
A bonus of a:b gives a new shares for every b held, so the new holding is holding × (1 + a ÷ b) and the ex-bonus price is cum-price × b ÷ (a + b). A split divides the price and multiplies the share count by old face value ÷ new face value. A rights issue is priced through TERP = (existing shares × market price + new shares × issue price) ÷ total shares. Bonus and split leave market capitalisation unchanged.
Syllabus location: Chapter 9: Corporate Actions. This chapter carries 5 marks in the 100-mark exam.
| Measure | Formula | Note |
|---|---|---|
| Holding after bonus | Holding × (1 + a ÷ b) | Bonus a:b means a new for every b held (usual Indian usage). If the question defines the ratio, follow it. |
| Ex-bonus price | Cum price × b ÷ (a + b) | Market cap stays the same. |
| Post-split price | Price ÷ (old face value ÷ new face value) | Share count rises by the same factor. |
| Theoretical ex-rights price (TERP) | (N × market price + n × issue price) ÷ (N + n) | N existing shares, n new shares. |
| Value of a right | Per existing share: cum-rights price − TERP. Per new share: TERP − issue price | Check which one the question asks for. |
| EPS after buyback | PAT ÷ (shares − shares bought back) | Assumes PAT is unchanged. |
An investor holds 200 shares when the company announces a bonus in the ratio 1:5 (1 bonus share for every 5 held). How many shares will the investor hold after the bonus?
Formula: Bonus of a:b means a new shares for every b held. Holding after bonus = holding × (1 + a ÷ b).
Working: Bonus shares = 200 × 1 ÷ 5 = 40. Total = 200 + 40 = 240 shares.
Common traps: 40 is only the bonus shares, not the new holding. 1,200 multiplies the holding by 6.
A company splits its shares of face value Rs. 10 into shares of face value Rs. 5. Before the split the share trades at Rs. 750. What is the theoretical post-split price?
Formula: Split factor = old face value ÷ new face value. Post-split price = old price ÷ split factor.
Working: 10 ÷ 5 = 2, so each share becomes 2 shares. 750 ÷ 2 = Rs 375.
Common traps: Market capitalisation does not change in a split: the share count doubles and the price halves. Rs 1,500 multiplies when it should divide.
An investor holds 350 shares and the cum-bonus price is Rs 700.
Bonus shares = 350 × 2 ÷ 5 = 140. New holding = 490 shares. Ex-bonus price = 700 × 5 ÷ 7 = Rs 500. Value before: 350 × 700 = 2,45,000. Value after: 490 × 500 = 2,45,000.
Price Rs 1,000 and 100 shares held.
Factor = 10 ÷ 2 = 5. New price = Rs 200. New holding = 500 shares. Value stays Rs 1,00,000.
Market price Rs 200. One new share for every 4 held.
TERP = (4 × 200 + 1 × 120) ÷ 5 = 920 ÷ 5 = Rs 184. Value of the right per new share = 184 − 120 = Rs 64. Per existing share = 200 − 184 = Rs 16.
PAT Rs 300 crore, 30 crore shares, buyback of 5 crore shares.
EPS before = 10. EPS after = 300 ÷ 25 = Rs 12.
The standard pivot is P = (H + L + C) ÷ 3 from the previous session. R1 = 2P − L and S1 = 2P − H. A fall of x% from a peak leaves peak × (1 − x). A rectangle's measured-move target is the breakout level plus (upside) or minus (downside) the height of the range. Chapter 15 is the largest chapter in NISM Series XV.
Syllabus location: Chapter 15: Technical Analysis. This chapter carries 15 marks in the 100-mark exam.
| Measure | Formula | Note |
|---|---|---|
| Pivot point | P = (H + L + C) ÷ 3 | Previous session's high, low and close. |
| First support and resistance | S1 = 2P − H; R1 = 2P − L | R1 uses the low, S1 uses the high. |
| Second support and resistance | S2 = P − (H − L); R2 = P + (H − L) | Classic (floor-trader) pivots. Other pivot systems use different formulas. |
| Fall from a peak | Peak × (1 − percentage) | A 10% fall from 500 is 450. |
| Fibonacci retracement of an up-move | High − (High − Low) × 38.2% / 50% / 61.8% | Measured down from the high. |
| Rectangle target | Breakout level ± height of the rectangle | Upside: resistance + height. Downside: support − height. |
| Head-and-shoulders target | Neckline − (head − neckline) | For a top pattern that breaks the neckline. Assumes a roughly horizontal neckline. |
A stock has consolidated in a range between support at Rs. 180 and resistance at Rs. 200. It breaks out above Rs. 200 on high volume. What is the measured-move target for the breakout?
Formula: Upside target = resistance + height of the rectangle. Downside target = support − height.
Working: Height = 200 − 180 = 20. Target = 200 + 20 = Rs 220.
Common traps: The height is added to the breakout level (resistance), not to the support. Rs 240 adds the height twice and Rs 160 is the downside target.
Yesterday a stock had a high of Rs. 612, a low of Rs. 594 and a close of Rs. 600. Using the standard formula, what is today's first resistance (R1)?
Formula: P = (H + L + C) ÷ 3. R1 = 2P − L. S1 = 2P − H.
Working: P = (612 + 594 + 600) ÷ 3 = 602.00. S1 = 2P − H = 592.00. R1 = 2P − L = 610.00.
Common traps: Rs 592 is S1 and Rs 602 is the pivot itself. R1 uses the low and S1 uses the high, which is easy to swap.
A stock peaked at Rs. 500 and then corrected by 10% from the peak. At what price is it now trading?
Formula: Price after a percentage fall = peak × (1 − percentage).
Working: 500 × (1 − 0.10) = Rs 450.
Common traps: Rs 550 adds 10% instead of removing it. Rs 455 divides by 1.10, which answers a different question.
Previous session: high 480, low 462, close 474.
P = (480 + 462 + 474) ÷ 3 = 472. R1 = 944 − 462 = 482. S1 = 944 − 480 = 464. R2 = 472 + 18 = 490. S2 = 472 − 18 = 454.
A stock rises from Rs 200 to Rs 350, a move of 150.
38.2% retracement: 350 − 57.3 = Rs 292.70. 50%: 350 − 75 = Rs 275. 61.8%: 350 − 92.7 = Rs 257.30.
Support Rs 360, resistance Rs 390, height 30. The price breaks below 360.
Target = 360 − 30 = Rs 330.
Head at Rs 520, neckline at Rs 470. The neckline breaks.
Height = 50. Target = 470 − 50 = Rs 420.
A stock falls 15% from Rs 800 to Rs 680 (800 × 0.85). A 20% rally from there gives 680 × 1.20 = Rs 816. Percentages do not reverse each other.
Contango means futures prices are above the spot price and rise with maturity, which reflects a positive cost of carry. Backwardation means futures prices are below spot, which happens when the convenience yield is greater than the cost of carry. In the cost-of-carry model, futures price = spot + storage + insurance + financing cost − convenience yield.
Syllabus location: Chapter 11: Fundamental Analysis of Commodities. This chapter carries 5 marks in the 100-mark exam.
| Measure | Formula | Note |
|---|---|---|
| Cost-of-carry futures price | Spot + storage + insurance + financing − convenience yield | Fair value of the futures contract. |
| Contango | Spot < near futures < far futures | Cost of carry dominates. |
| Backwardation | Spot > near futures > far futures | Convenience yield exceeds carry cost. |
| Basis (as used here) | Spot − futures | Negative in contango. Some texts define it the other way, so check the question. |
| Implied convenience yield | Spot + carry costs − futures price | Positive when the futures price is below full carry. |
A commodity trades at Rs. 84 in the spot market, Rs. 86 for one-month futures and Rs. 88 for three-month futures. What does this price structure indicate?
Formula: Contango: futures above spot and rising with maturity. Backwardation: futures below spot.
Working: 84 < 86 < 88, so the curve slopes upward: contango. The higher deferred prices reflect the cost of carry (storage, insurance and financing).
Common traps: Futures above spot is contango, not backwardation. Backwardation needs futures below spot, which happens when the convenience yield is greater than the cost of carry.
Spot Rs 92, one-month futures Rs 90, three-month futures Rs 87.
Prices fall as maturity lengthens: backwardation.
Spot Rs 5,000. Storage and insurance total Rs 150, financing cost is Rs 200.
Fair futures = 5,000 + 150 + 200 = Rs 5,350.
Fair futures price Rs 5,350 but the futures trade at Rs 5,450.
Buy the commodity at spot, finance and store it, and sell the futures. The locked-in gain is 5,450 − 5,350 = Rs 100.
Spot Rs 62,400 and futures Rs 62,700.
Basis = 62,400 − 62,700 = −300. A negative basis with futures above spot is contango.
Spot Rs 5,000, carry costs Rs 350, futures Rs 5,250.
Convenience yield = 5,000 + 350 − 5,250 = Rs 100.
The exact real interest rate is (1 + nominal) ÷ (1 + inflation) − 1. The shortcut nominal − inflation is only an approximation, and the gap grows as rates rise. Real GDP growth uses the same structure with the GDP deflator. When a question says exact or Fisher, use the ratio.
Syllabus location: Chapter 5: Economic Analysis. Chapter 5 carries 5 marks. Real-return calculations also appear in Chapter 12 (Risk and Return), which carries 7 marks.
| Measure | Formula | Note |
|---|---|---|
| Real rate (exact) | (1 + nominal) ÷ (1 + inflation) − 1 | Fisher relationship. |
| Real rate (approximation) | Nominal − inflation | Close only when rates are low. |
| Nominal from real | (1 + real) × (1 + inflation) − 1 | |
| Inflation from an index | (CPI this year − CPI last year) ÷ CPI last year | |
| Real GDP growth | (1 + nominal growth) ÷ (1 + deflator inflation) − 1 |
The nominal interest rate is 9% and inflation is 4%. Using the exact (Fisher) relationship, what is the real rate of return?
Formula: Real rate = (1 + nominal) ÷ (1 + inflation) − 1.
Working: 1.09 ÷ 1.04 − 1 = 1.0481 − 1 = 4.81%.
Common traps: The shortcut 9% − 4% = 5.00% is only an approximation. When a question says exact or Fisher, use the ratio. 13.00% adds the two rates.
Nominal 11%, inflation 5%.
1.11 ÷ 1.05 − 1 = 0.05714 = 5.71%. The approximation 11 − 5 = 6% is slightly higher.
Nominal 7.5%, inflation 6%.
1.075 ÷ 1.06 − 1 = 1.42%. The approximation is 1.5%.
CPI rises from 152.4 to 160.9.
(160.9 − 152.4) ÷ 152.4 = 8.5 ÷ 152.4 = 5.58%.
Nominal GDP grows 12% and the GDP deflator rises 5%.
1.12 ÷ 1.05 − 1 = 6.67%.
An investor wants a 3% real return and expects 5% inflation.
(1.03 × 1.05) − 1 = 8.15%.
Sharpe ratio = (portfolio return − risk-free rate) ÷ standard deviation of the portfolio's returns. For a fund that returned 18% with a 10% standard deviation when the risk-free rate was 6%, it is (18 − 6) ÷ 10 = 1.20.
Both measure excess return per unit of risk. Sharpe uses total risk (standard deviation), so it suits a standalone portfolio. Treynor uses beta, which is market risk only, so it suits a portfolio that is one part of a well-diversified holding.
Required return = risk-free rate + beta × (expected market return − risk-free rate). With rf = 6%, Rm = 11% and beta = 1.25, the required return is 6 + 1.25 × 5 = 12.25%.
It is the expected market return minus the risk-free rate. If the market is expected to return 11% and the risk-free rate is 6%, the premium is 5 percentage points.
Add share capital and reserves to get net worth, divide by the number of shares (share capital ÷ face value) to get book value per share, then divide the market price by that. With Rs 60 crore capital, Rs 260 crore reserves, face value Rs 10 and a Rs 210 price, P/B is 210 ÷ 53.33 = 3.94 times.
PEG compares the P/E with expected earnings growth. A stock at a P/E of 18 with 20% expected growth has a PEG of 0.90. Lower values mean you pay less per unit of growth, though PEG depends on the growth forecast being right.
Use the basis the question states. When it says average equity, average the opening and closing balances. For PAT of Rs 90 crore and equity of 700 and 740, average equity is 720 and ROE is 12.50%.
EBIT is smaller than interest expense, so operating profit does not cover the interest bill. A ratio of 2.67 means EBIT is 2.67 times interest.
No. The number of shares rises and the price falls in proportion, so market capitalisation is unchanged. A holder of 200 shares who receives a 1:5 bonus owns 240 shares at a correspondingly lower price.
A bonus issue gives extra shares by capitalising reserves and leaves face value unchanged. A split cuts the face value (for example Rs 10 to Rs 5) and multiplies the shares. Both lower the price per share and neither changes market capitalisation.
The pivot is the average of the previous session's high, low and close, (H + L + C) ÷ 3. R1 = 2 × pivot − low and S1 = 2 × pivot − high. With a high of 612, low of 594 and close of 600, the pivot is 602, R1 is 610 and S1 is 592.
Measure the height of the rectangle (resistance − support) and add it to the resistance for an upside breakout, or subtract it from the support for a downside break. A range of 180 to 200 breaking upward has a target of 200 + 20 = Rs 220.
Contango is when futures prices are higher than the spot price and increase with maturity. A commodity at Rs 84 spot, Rs 86 for one month and Rs 88 for three months is in contango. The gap reflects storage, insurance and financing costs.
Backwardation occurs when futures trade below spot, usually because holders value having the physical commodity now. In cost-of-carry terms, the convenience yield is greater than the cost of carry.
The Fisher equation links nominal, real and inflation rates: (1 + nominal) = (1 + real) × (1 + inflation). Rearranged, the real rate is (1 + nominal) ÷ (1 + inflation) − 1.
Divide 1 plus the nominal rate by 1 plus the inflation rate, then subtract 1. With a 9% nominal rate and 4% inflation, 1.09 ÷ 1.04 − 1 = 4.81%.
Take the two free 20-question NISM XV numerical tests with a free account. Scoring copies the real exam: +1 for a correct answer and −0.25 for a wrong one, and every answer gets a worked solution when you finish.
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