Foundations of Finance

A share listed in Tokyo shows a best bid of ¥2,495 and a best ask of ¥2,505. What is the bid-ask spread as a percentage of the mid price?

A fund must sell 3,000 shares at once with a market order. The best ask is $10.04. The bids are:

• 1,000 shares at $10.00
• 1,000 shares at $9.98
• 2,000 shares at $9.95

How much does the sale cost the fund against the mid price, in dollars?

A fund returns 15%, then −10%, then 5% over three years. What is its total return over the three years, in %?

Four deals settle today. In which one does the company or government that issued the security receive the cash?

A fund buys shares of a US company on Monday on the exchange. Which describes what normally happens next?

Lakeside Bank, in € millions, over one year:

• Loans: €600m earning 6.00%
• Securities: €250m earning 3.50%
• Reserves: €150m earning 4.00%
• Deposits: €750m costing 2.25%
• Wholesale funding: €150m costing 5.00%

All the assets earn interest. What is its net interest margin, in %?

An Australian motor insurer earns A$1,200m of premiums. Its loss ratio is 74% and its expense ratio 29%. It holds the money for claims for 1.5 years on average and earns 4% a year on it. What is its operating result (underwriting result plus investment income on the float), in A$ millions?

A hedge fund runs 5× leverage: each $1 of equity supports $5 of assets, and it borrows the rest at 4%. Its assets return −6% this year. What is the return on its equity, in %?

A bank holds US$27bn of CET1 capital against US$400bn of risk-weighted assets. Under Basel III, which is right?

A clearing member defaults and closing out its positions costs the CCP €380m. The defaulter posted €250m of initial margin and €40m to the default fund; the CCP has €30m of its own capital in the waterfall; the other members' default fund contributions total €500m. How much do the surviving members lose, in € millions?

A couple in Perth borrow A$400,000 over 25 years at 6% a year, compounded monthly, repaid in equal payments at the end of each month. What is the monthly payment, in A$?

A rate is quoted as 6% a year with annual compounding. What continuously compounded rate gives the same growth, in %?

A UK company deposits £8,000,000 from 1 April to 30 September 2026 at 4.25% a year, simple interest, ACT/365F. How much interest does it earn, in £?

A savings account in South Africa pays 7% a year and inflation is 4.5%. What is the exact real rate, in %?

The 1-year spot rate is 3.0% and the 2-year spot rate is 3.6%, both with annual compounding. What one-year rate, starting in one year, does this curve imply, in %?

A 5-year bond pays a 6% coupon once a year and repays 100 at maturity. The market yield for it is 5%. What is its price, per 100 of face value?

An 8-year bond with a 4% annual coupon trades at 94. Which ordering is right?

A portfolio manager in New York holds $20m face value of a bond priced at 97.50 with a modified duration of 7.2. What is the position's DV01, the money change in value for a one basis point move in yield, in $?

A long bond has a modified duration of 8 and convexity of 90. Its yield jumps by 1.5 percentage points. Using duration and convexity, what is the estimated percentage change in its price?

A 5-year corporate bond yields 5.9% and the 5-year government bond 4.1%. You estimate a 1.2% yearly default probability and a 55% loss given default. How many basis points of the spread are left over after expected loss?

A Dutch utility has just paid a dividend of €2.40 a share. Dividends are expected to grow 3.5% a year for ever, and investors require 8.5%. What is the share worth today, in €?

Alpina Logistics has 200 million shares at €25, €1,500m of debt, €300m of cash and EBITDA of €800m. What is its EV/EBITDA multiple?

A share's daily returns have a standard deviation of 1.2%. Assuming 252 trading days a year and independent days, what is its annualised volatility, in %?

A fund borrows and sells 4,000 shares at $60. The borrow fee is 3% a year on the starting value, ACT/360. While the loan is open the company pays a dividend of $0.75 a share. After 120 days the fund buys the shares back at $51 and returns them. What is its net profit, in $?

A UK company with 50 million shares at £4.20 offers 1 new share for every 5 held, at £3.00. What is the theoretical ex-rights price (TERP), in £?

EUR/USD is 1.0850 and USD/JPY is 152.40. Ignoring spreads, what is EUR/JPY?

AUD/USD spot is 0.6600. One-year interest rates are 4.5% in US dollars and 3.9% in Australian dollars, annual compounding. What is the one-year forward AUD/USD rate, to four decimals?

A 182-day US Treasury bill with face value $1,000,000 is quoted at a discount rate of 4.40%. What do you pay for it, in $?

Crude oil is $80 a barrel for immediate delivery and $76 for delivery in six months. A commodity fund holds long futures and rolls them forward each month. Which is right?

A Japanese investor buys US shares that return 8% in dollars over a year. Over the same year the dollar falls 5% against the yen. What is her return in yen, in %?

A share trades at $60. It will pay a $1.50 dividend in six months. The interest rate is 4% a year, annual compounding. What is the fair one-year forward price, in $?

A trader buys one crude oil future of 1,000 barrels at $75. Initial margin is $6,000 and maintenance margin $4,500. The next day it settles at $73.20. How much cash must the trader pay in, in $?

A company pays fixed at 3.6% and receives SOFR on a $50m interest rate swap, settled once a year (take the year fraction as 1). SOFR compounded over the year comes to 4.1%. What net amount does the company receive, in $? (Negative if it pays.)

A one-year European call with strike $100 costs $7.20. The share is at $95, pays no dividends, and the interest rate is 5% a year, annual compounding. What should the one-year put with the same strike cost, in $?

The day before a company reports results, the market expects a big move but not which way. Its share price is unchanged, but the volatility priced into its options jumps. What happens to its calls and puts?

A euro area bank has €18bn of CET1 capital and €3bn of Additional Tier 1, so Tier 1 is €21bn. Its risk-weighted assets are €220bn and its leverage exposure €600bn. What is its Basel leverage ratio, in %?

A Singapore bank has operating income of S$4,800m, operating costs of S$2,880m and impairments of S$400m. What is its cost-income ratio, in %?

On 1 May a customer buys a 12-month home insurance policy for NZ$1,800. The insurer's financial year ends on 31 December. How much of the premium is earned in this financial year, in NZ$ (spread evenly by month)?

A European insurer has IFRS equity of €4,800m. On the Solvency II basis it removes €400m of intangibles, its technical provisions are €600m lower, it counts €900m of qualifying subordinated debt, and it deducts €250m of foreseeable dividends. Its SCR is €3,100m. What is its solvency ratio, in %?

Depositors withdraw £2bn from a bank. It has too little cash, so it sells government bonds carried at £2bn on its balance sheet, but in the rush they fetch only £1.8bn. What happens to its equity?

A bank holds €500m (market value) of government bonds with a modified duration of 6.2, financed in repo at a 3% haircut. Yields rise by 80 basis points overnight. Using duration to revalue the bonds, and with the haircut unchanged, how much cash must the bank hand back to its repo lender, in € millions?

Stay with that bank. Its Tier 1 capital is €1.2bn and its leverage exposure €30bn. The bonds are held at fair value, so the loss goes through its capital. Rates keep rising and markets get nervous. Which combination is most likely?

A life insurer holds €10bn of bonds with a modified duration of 6. Its technical provisions are valued at €9bn with a modified duration of 10. Interest rates fall by 0.5 percentage points. Using duration, by how much does the gap between assets and liabilities (its equity on this basis) change, in € millions? (Negative for a fall.)

A 5-year bond issued by a retailer yields 6.35%; the 5-year government bond yields 4.15%. Treat the whole spread as the price of default risk, as a CDS spread is read, with a 40% recovery rate. What yearly default probability does the market imply, in %?

A Japanese insurer converts ¥1.5bn into dollars at USD/JPY 150 and places it for one year at 5.0%. At the same time it sells the dollars it will receive forward for yen. The one-year yen rate is 0.5%, and the forward is priced by covered interest parity (annual compounding). What is the insurer's one-year return in yen, in %?

A pension fund holds an index tracker with the index at 5,000. It buys one-year put options on the index with a strike of 4,600, paying 120 index points. Over the year the index falls 25%. Ignoring dividends and interest, what is the return on the fund's combined position (index plus puts), measured against the starting index level, in %?