Any help solving the following problem is welcomed - formulas, web
sites, etc.

Having heard about IPO underpricing, I put in an order to my broker
for 1,000 shares of every IPO he can
get me. After 3 months, my investment record is as follows:						
						
IPO	Shares 	Price per				
return	Allocated to Me	Share	Initial			
A	500	$10 	7%			
B	200	20 	12%			
C	1,000	8 	-2%			
Enter formulas to calculate the requirements of this problem.						
						
a. What is the average underpricing of this sample of IPOs?						
Average underpricing	FORMULA					
						
b. What is the average initial return on my "portfolio" of shares
purchased from the four IPOs I bid on?
Calculate the average initial return weighting by the amount of money
invested in each issue.
						
	Investment	Initial				
	(Shares x price)	Return	Profit			
A	FORMULA	7%	FORMULA			
B	FORMULA	12%	FORMULA			
C	FORMULA	-2%	FORMULA			
Total	$0 		$0 			
						
Average return	FORMULA					
						
c. Why have I performed so poorly relative to the average initial
return on the full sample of IPOs? What
lessons do you draw from my experience?

Thank you for the additional finance question.

Question a.: the average underpricing would be the average of the
returns, which is equal to (7% + 12% + -2%)/3 = 5.67%

Question b.: the average return achieved would be the average of the
returns weighted by the number of shares purchased.  This is equal to
[500 (7%) + 200 (12%) + 1000 (-2%)]/(500 + 200 + 1000] = 2.29%

Question c.: "This underpricing does not imply that any investor can
expect to become wealthy by purchasing unseasoned stock from the
underwriters, for if the issue is attractive, the underwriters will
not have enough stock to go around."

"Suppose that you could always be sure of getting your fair share of
any issue that you applied for without having to ingratiate yourself
with the investment banker.  Does that mean that you could make
handsome profits on average by applying for an equal amount of each
issue?  Unfortunately, no.  If an issue is cheap, it is also likely to
be oversubscribed; if it is dear, it is likely to be undersubscribed. 
So you will receive a small portion of the cheap issues and a large
proportion of the dear ones."

Principles of Corporate Finance, fourth edition, by Brealey and Myers,
McGraw-Hill, Inc., 1991, pages 345-346

This phenomenon is exactly what has happened to this investor.  The
larger amount of poorly performing shares purchased relative to the
smaller amounts of the better performing shares decreased the weighted
average return by over 50% from the one that would have been achieved
with equal amounts of shares.

Sincerely, 

Wonko

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Request for Answer Clarification by boobee-ga on 10 Jul 2003 19:33 PDT

Hi again Wonko,

Following are the profits I got when using your formulas.  Is this
correct?

Enter formulas to calculate the requirements of this problem.					
					
a. What is the average underpricing of this sample of IPOs?					
Average underpricing	6%				
					
b. What is the average initial return on my "portfolio" of shares
purchased from the four IPOs I bid on?
Calculate the average initial return weighting by the amount of money
invested in each issue.
					
	Investment	  Initial			
	(Shares x price)  Return	Profit		
A	$500 	              7%	 $35 		
B	200 	             12%	 $20 		
C	1,000 	             -2%        $980 		
Total	$1,700 		              $1,035 		
					
Average return	2.29%

---

Clarification of Answer by wonko-ga on 10 Jul 2003 20:54 PDT

Initial investment A = 500*10 = 5000.  Profit = 0.07*5000 = 350.
Initial investment B = 200*20 = 4000.  Profit = 0.12*4000 = 480.
Initial investment C = 1000*8 = 8000.  Profit = -0.02*8000 = -160.

Net profits = 350+480+(-160) = 670.  Average return = 670/17000 =
3.94% (this includes weighting by share price, which your formula
requires).

Sincerely,

Wonko