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Work out average daily volume and float, and explain how liquidity is measured

CFA® Level I · Equity Investments · Equity Issuance and Trading · EQ.9.b

The idea

Liquidity is how easily a position can be traded without moving the price. Float is the number of shares actually available to trade: shares outstanding less those held by insiders, governments, strategic holders or under lock-up. Average daily volume (ADV) is total shares traded over a window divided by the number of trading days, and analysts often drop unusual days, such as index rebalancing, that would flatter it. Relating the two gives turnover, ADV divided by float. Other measures include the bid-ask spread, market depth at the best prices and the estimated price impact of a large order. A useful practical figure is days to trade: position size divided by the number of shares the trader is willing to trade each day, which is a chosen fraction of ADV.

A practice question

From the question bank, with the reason each wrong option is wrong.

Company C has 200 million shares outstanding. Its founders hold 40 million and a strategic corporate investor holds 20 million, none of which are expected to trade. What is the float?

  1. 140 million shares — correct
  2. 160 million sharesWhy not: Subtracting only the founders' 40 million and forgetting the strategic holder's 20 million, which are also closely held.
  3. 60 million sharesWhy not: That is the closely held total, the shares that are not available to trade, rather than the float.

Float = shares outstanding less closely held shares = 200 - 40 - 20 = 140 million shares.

A harder one

A share traded 420,000, 380,000, 510,000, 290,000 and 400,000 shares over five days. A fund holds 1.2 million shares and will trade no more than 25% of average daily volume per day. How many days will it need to sell the position?

  1. 3 daysWhy not: Dividing by the full average daily volume of 400,000 shares. The 25% participation limit cuts daily sales to 100,000.
  2. 2.4 daysWhy not: Applying the 25% limit to the five-day total of 2.0 million shares instead of the daily average.
  3. 12 days — correct

ADV = 2,000,000 / 5 = 400,000. Daily sales limit = 0.25 x 400,000 = 100,000. Days = 1,200,000 / 100,000 = 12.

The hardest tier

Stock X has 500 million shares outstanding, a float of 400 million and ADV of 2.0 million. Stock Y has 300 million outstanding, a float of 100 million and ADV of 1.5 million. Relative to float, which trades more actively, and at what daily turnover?

  1. Stock X, at 0.5% of floatWhy not: Ranking the stocks by raw share volume. X trades more shares, but a smaller fraction of what is available to trade.
  2. Stock Y, at 0.5% of sharesWhy not: Dividing Y's volume by shares outstanding, which counts 200 million closely held shares that never trade.
  3. Stock Y, at 1.5% of float — correct

Turnover relative to float: X = 2.0 / 400 = 0.5% a day; Y = 1.5 / 100 = 1.5% a day. Y's float turns over three times as fast.

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