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Put-Call Parity

The no-arbitrage relationship C - P = S - PV(K) that must hold for European options on a non-dividend-paying stock.

Definition

Put-call parity states that for European options with the same underlying, strike (K), and expiry, the call price (C) minus the put price (P) equals the current stock price (S) minus the present value of the strike price discounted at the risk-free rate over the option's life. Rearranged: C + PV(K) = P + S. If parity breaks, a riskless arbitrage exists - for example, if the call is overpriced relative to the put, a trader can sell the call, buy the put, buy the stock, and borrow PV(K) to lock in a profit with no net investment. In practice, dividends and early-exercise features of American options create small deviations from the parity formula, but arbitrageurs keep prices tightly aligned. For the CIRE, put-call parity is tested as a conceptual check: given three of the four variables (C, P, S, K), solve for the fourth, or identify which option is relatively over- or underpriced.

Source

Options theory; verify specific formula emphasis in CIRE blueprint; Montreal Exchange educational resources

Where this shows up on the CIRE

  • Outcome 5.3

Test yourself

Two real CIRE-bank questions on this exact outcome. Click to reveal the answer and the rule citation.

  1. 1

    Statistics Canada releases a monthly report showing the Consumer Price Index (CPI) increased by 4.1% year-over-year, above the Bank of Canada's 2% target. Which economic indicator has been reported, and what is its primary significance for investment analysis?

    Outcome 5.3 · click for answer

    A.The CPI measures the change in the price of a fixed basket of consumer goods and services over time; a reading above the Bank of Canada's 2% target signals that inflation is running hot, which may lead the Bank to raise its overnight rate to reduce demand and bring inflation back toward target.Correct
    B.The CPI measures the trade balance; a 4.1% reading means Canada is importing more than it exports.
    C.The CPI measures corporate earnings growth; a 4.1% reading signals that corporate profits are rising.
    D.The CPI measures unemployment; a 4.1% reading means unemployment has risen significantly.

    The Consumer Price Index (CPI) published by Statistics Canada measures changes in the price of a fixed basket of goods and services purchased by Canadian households. It is Canada's primary inflation indicator. The Bank of Canada targets inflation of 2% (within a 1% to 3% control range). A CPI reading of 4.1% year-over-year indicates above-target inflation, which historically leads the Bank to raise its policy rate to cool demand. This has direct implications for fixed income prices, equity valuations, and currency movements.

  2. 2

    A registrant is explaining economic indicators to a client. The client asks what the Consumer Price Index measures and why it matters for investment decisions. Which response is most accurate?

    Outcome 5.3 · click for answer

    A.The CPI measures the total market value of all goods and services produced in Canada during a quarter, making it the primary measure of economic output.
    B.The CPI measures changes in the average prices of a fixed basket of goods and services purchased by Canadian households and is the primary indicator used to track inflation, which directly influences interest rate decisions and the real return on fixed income investments.Correct
    C.The CPI measures unemployment rates among manufacturing workers and is used exclusively by labour market economists.
    D.The CPI measures the profitability of the S&P/TSX Composite Index constituent companies and is used to forecast equity market returns.

    The Consumer Price Index tracks changes in the average price of a representative basket of goods and services purchased by Canadian households, serving as the primary measure of inflation in Canada. Inflation directly affects investment decisions: it erodes the real return on fixed income securities, influences the Bank of Canada's policy rate decisions, and affects the purchasing power of savings. GDP measures total economic output, unemployment measures labour market conditions, and corporate profitability is tracked through earnings reports; not the CPI.

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