Question

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 $1,200, what arbitrage opportunity is available? What trades would you make?

	a.	buy one ETF and sell 2 shares of APPL, 10 shares of GOOG, and 1 share of MSFT.
	b.	sell one ETF and buy 3 shares of APPL, 2 shares of GOOG, and 10 shares of MSFT.
	c.	buy one ETF and sell 2 shares of APPL, 1 share of GOOG, and 10 shares of MSFT.
	d.	do nothing, no arbitrage opportunity exists.
	e.	sell one ETF and buy 2 shares of APPL, 3 shares of GOOG, and 10 shares of MSFT.

Answer 1

The value of etf should be = sum of value of shares in the etf

Value of shares of apple held =2 shares *200.23=400.46

Value of shares of google held =1 share * 570.51=570.51

Value of shares of microsoft held =10 shares * 29.61=296.1

Hence the value of etf should be =400.46+570.51+296.1

=1267.07

Given the value of etf is 1200

Hence etf is under valued. So one should buy etf and sell the shares in the etf to get a arbitrage profit of =1267.07-1200=67.01

Hence option c is correct that is you should buy 1 etf and sell 2 shares of apple 1 share of google and 10 shares of microsoft

Hence the inflow by selling shares =1267.07

And the outflow to purchase etf =1200

Net inflow =67.07

Other options are incorrect because -

Option a is incorrect becuase if you sell 2 shares of apple 10 shares of google and 1 share of microsoft the value of short posistion =2*200.23+10*570.51+1*29.61= 6135. 17

Where as long position will be in etf which has 2 shares of apple, 1 share of google and 10 share of microsoft

Hence there will be mismatch is the weightage of stocks

Option b and e is incorrect becuase etf is under valued and should not be sold

Option d is incorrect because there exists arbitrage opportunity of 67.07 as shown above