Question

2. Suppose an ETF has a NAV of $12 at t=0 and $12.10 at t=1. At t=0, the fund sells at a premium of 0.5% to NAV; at t=1, the fund sells at a discount of 0.2% to NAV. Further suppose that the ETF paid income of $1.50 per share. a. What is the ETF return to an investor who buys at t=0 and sells at t=1?

Answer 1

An ETF's market value is the price at which it can be bought or sold in the market.

An ETF's NAV is Net Asset Value - i.e. each unit's share of net assets and cash at the end of each day.

There can be difference between these two because of investor's expectations regarding an ETF and it reflects in the trading. Market price is reflected as Premium or Discount to the NAV.

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The return required to calculate here is Holding Period Return.

Formula for the same is:

(EV - BV + Income)/ BV

where,

EV = Ending value or Sale Price

BV = Beginning value or Purchase Price

Now, let us calculate the Purchase and Sale price of this ETF.

At t = 0

the fund sells at a premium of = 0.5% to NAV

NAV = $12

therefore, market price = $ 12 + ($12 * 0.5%) = 12 + 0.0600 = 12.0600

Since investor purchased on t=0,

Purchase Price at t=0 is $12.0600 per share

At t = 1

the fund sells at a discount of = 0.2% to NAV

NAV = $12.10

therefore, market price = $ 12 - ($12 * 0.2%) = 12 - 0.0242 = 12.0758

Since investor sold on t=1,

Sale Price at t=1 is $12.0758 per share

Income during this period = $1.50 per share

Return is calculated as:

( Sale Price - Purchase Price + Income ) / Purchase Price

= (12.0758 -12.0600 + 1.5000) / 12.0600

= 0.1257

Return on investment = 12.57%