## Sunday, 7 May 2017

### The Arbitrage Risk Equation Warren Learned from Benjamin Graham

An example of arbitrage.

Announcement of the \$55 a share tender offer
Stock was trading at \$44 a share before the announcement.
After the announcement, you are buying the stock at \$50 a share.
Likelihood of Deal Happening 90%.

1,  Determine what is your potential return?

Tender offer \$55 a share
You can buy the stock at \$50 a share
Your arbitrage investment has a projected profit (PP) of \$5 a share
This gives a 10% projected rate of return on your \$50 investment.

2.  What is the likelihood that the event will occur as a percentage?

Does it have a 30% chance of being completed?  Or a 90% chance?

Likehood of Deal Happening = 90%

APP
= Projected Profit x Likelihood of Deal Happening
= PP x LDH
= \$5 x 90%
= \$4.50

4. Adjusted Projected Rate of Return (APRR)

APRR
= Projected Profit / Your Investment
= PP / I
= \$4.50 / \$50
= 9%.

5.  What is the risk of the deal falling apart?

What is your risk of loss?

If the deal fails to be completed, the per share price of the stock will return to the trading price it had before the tender offer was announced.

If the stock was trading at \$44 a share before the announcement of the \$55 a share tender offer and after the announcement, we are buying the stock at \$50 a share, we have a downside risk of \$6 a share if the deal falls apart and the price of the company's stock returns to \$44 a share (\$50 - \$44 = \$6).

Thus, if the deal falls apart, you have a projected loss of \$6 a share.

Projected Loss \$6 a share
Likelihood of the deal falling apart (LDFA) 10%

Adjusted projected loss (APL) of \$0.60 a share (\$6 x 0.1 = \$0.60)

RAPP
= APP - APL
= \$4.50 - \$0.60
= \$3.90

8.  Risk-adjusted Projected Rate of Return (RAPRR)

RAPRR
=Risk Adjusted Projected Profit / Investment
=RAPP/I
= \$3.90 / \$50
= 7.8%

Is a risk-adjusted projected rate of return of 7.8% an enticing enough return for us?

If it is, we make our investment.

[If the RAPP is a negative number, walk away from the deal.]

It is probably not necessary to do these calculations, though they serve as a means to help you think about the potential of the opportunity presented.

A successful arbitrage operation has more to do with the art of weighing the different variables than attempting to quantify them down to a hard scientific equation that tells you when to buy and when to sell.

These variables themselves can change and often they are simply unique to that situation.

They are tools that can be helpful if used properly.

-------------------------------------

Summary

Announcement of the \$55 a share tender offer
Stock was trading at \$44 a share before the announcement.
After the announcement, you are buying the stock at \$50 a share.
Likelihood of Deal Happening 90%.

1,  Determine what your potential return is?

Your arbitrage investment has a projected profit (PP) of \$5 a share
This gives a 10% projected rate of return on your \$50 investment.

2.  What is the likelihood that the event will occur as a percentage?

Likehood of Deal Happening = 90%

APP
= Projected Profit x Likelihood of Deal Happening
= PP x LDH
= \$5 x 90%
= \$4.50

4. Adjusted Projected Rate of Return (APRR)

APRR
= Projected Profit / Your Investment
= PP / I
= \$4.50 / \$50
= 9%.

5.  What is the risk of the deal falling apart?

Thus, if the deal falls apart, you have a projected loss of \$6 a share.

Projected Loss \$6 a share
Likelihood of the deal falling apart (LDFA) 10%

Adjusted projected loss (APL) of \$0.60 a share (\$6 x 0.1 = \$0.60)

RAPP
= APP - APL
= \$4.50 - \$0.60
= \$3.90

8.  Risk-adjusted Projected Rate of Return (RAPRR)

RAPRR
=Risk Adjusted Projected Profit / Investment
=RAPP/I
= \$3.90 / \$50
= 7.8%

Is a risk-adjusted projected rate of return of 7.8% an enticing enough return for us?

If it is, we make our investment.

[If the RAPP is a negative number, walk away from the deal.]