Question

10. An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider an ETF for which each share represents a portfolio of two shares of Apple Inc. (APPL), one share of Google (GOOG), and ten shares of Microsoft (MSFT). Suppose the current stock prices of each individual stock are as shown below:

Stock	Price
APPL	$200.23
GOOG	$570.51
MSFT	$29.61

If the ETF is currently trading for $1200, what arbitrage opportunity is available? What trades would you make?

Answer 1

Here in this question

NAV of an ETF share = Value of assets in an ETF share

NAV of the ETF = Value of 2 shares of Apple + Value of 1 share of Google + Value of ten shares of Microsoft

= 2 x 200.23 + 1 x 570.51 + 10 x 29.61 = 400.46 + 570.51 + 296.10 = 1267.07

Also one share of ETF is trading at $1200

Since ETF is trading at a discount to its NAV , there exists an arbitrage opportunity

Arbitrage is always exploited by going long on security trading at discount and short on the other security

Since NAV is more than current price of ETF, therefore we will short sell (or sell) 2 shares of apple,1 share of google and ten shares of Microsoft to receive 1267.07 based on current market prices. Then we will buy a share of ETF for $1200 and in process make profit = 1267.07 - 1200 = 67.07

Trades	Cash Flow
Short sell (or Sell) individual shares	1267.07
Buy a share of ETF	-1200
Profit	67.07