Discounts and Premiums · Closed End Funds

Discount history adds context to today’s valuation. A z score expresses distance from a historical average, but it cannot tell you whether the old average still makes sense.

Define the series before calculating

Use a consistent signed valuation series, such as market price divided by NAV, minus one. A 10% discount is then minus 10%. Choose an observation frequency and lookback period. Mixing daily and monthly observations, or positive discount magnitudes with signed values, can reverse the interpretation.

Work through the statistic

Suppose the historical average signed valuation is minus 6% and its standard deviation is 2 percentage points. Today’s valuation is minus 10%. Subtracting the average gives minus 4 percentage points. Dividing by 2 gives a z score of minus 2. On this convention, today’s price is more discounted than the historical average.

A statistical distance is not a forecast

A z score of minus 2 does not establish a particular probability of recovery. The observations may be skewed, correlated or affected by a structural change. A distribution cut, new manager, changed leverage policy or deteriorating asset quality can make the historical average less relevant. A small standard deviation can also produce a dramatic score from a modest price move.

Use several pieces of evidence

Compare multiple windows and inspect the actual discount chart. Note corporate actions and valuation methodology changes. Ask whether similar funds moved at the same time. A wider discount across an entire sector may reflect a changed economic environment rather than an isolated mispricing.

Create a dated research record with today’s NAV, price, discount, chosen average and standard deviation. Add a short explanation of what changed in the fund. This prevents a screening statistic from becoming a substitute for research and makes later review possible.

Try it yourself

The average signed valuation is minus 8%, the standard deviation is 3 percentage points, and today’s valuation is minus 5%. What is the z score?

Show the worked answer

The difference is positive 3 percentage points, so the z score is positive 1. The fund is less discounted than its historical average on this convention. That is not proof it is overpriced.

Further reading

Educational material, not a recommendation to buy or sell a fund. Numerical examples are hypothetical. Fund terms, investor eligibility and tax treatment vary by product, account and jurisdiction.

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