# Decision Model



## Oorang (Jan 10, 2007)

This didn't really seem like an Excel Question, just more if a "What is you opinion" type thing. 

Does this seem like a good decision model?
Decided max risk threshold (R)
Decided min gain worth risk for (G_0)
Calculate Possible Gain of Plan (G_1)
Calculate Possible Loss of Plan (L_1)
Calculate Probability of Gain (G_2)
Calculate Probability of Loss (L_2 = 1 - G_2)

If  ((G_1*G_2)>(L_1*L_2)) and (L_2 < R) and (G_1>G-0)  then Execute Plan?


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## Oaktree (Jan 10, 2007)

There's merit to your approach, but, IMO, the only real answer to your question is "maybe", as there are several questions you need to ask/things to consider.  

Here are 3 off the top of my head:

1) Very few real world situations are clean cut enough to know the exact probability of gain vs. loss and the exact gain/loss expected in each case.  Even guessing at the distribution is a feat.  Plus, natural tendency is to over/underestimate potential gains and under/overestimate potential losses according to one's preference toward seeing the project get approved (just ask any marketing guy how much incremental sales his IFR will generate...)

2) Strategically, the best projects won't always meet those criteria (as with hurdle rates)  

3) Your G_0 cannot be an absolute number... it has to be relative to the investment required.  (e.g. if I told you there was a 99% chance of making $500 and a 1% chance of losing $5, your criteria would be met, and it would be a good idea....unless I told you it required a $300K investment, in which case it probably isn't the best use of your $300K).


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## Bartek (Jan 10, 2007)

Hi,



> If  ((G_1*G_2)>(L_1*L_2)) and (L_2 < R) and (G_1>G-0)  then Execute Plan?



Looks pretty straightforward: expected value criterion combined with constraints. However, it seems a bit strange to define risk threshold in terms of probability rather than value (since you compare it to L_2). Such decision may produce strange decisions like rejecting a plan with very high expected value but relatively high skewness (favorable lottery).


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## Oorang (Jan 10, 2007)

Hey Oaktree, I was hoping you'd weigh in on this  
1. I expect to implement a model for deciding each variable as well, but before I drilled down to that level, I thought I'd make sure I had the overall concept first. So of that information can be provided by good research, but I realize some will have to be educated guesswork. (For gains.) But good planning can truly limit risk of lossage, because you don't execute a plan that can't be completly backed out of if need be. You set up a loss threshold to throw the switch and kill it. 
2/3. I completly agree with your point on G_0

Bartek. I hadn't originally made that combination until I realized it would support certain things that may not be all that great from certain perspectives (like the lottery). Which is why I introduced the R variable. If you turn that way down, you will find the lottery looks like a great idea


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## Andrew Fergus (Jan 10, 2007)

I would have through a lottery situation would never pass the (G_1*G_2)>(L_1*L_2) test given not all of the take is returned as prizes.  Take for example a lottery where there are 100 tickets at $1 each and there is one prize of $70 ($30 used to cover expenses).  G1*G2 = 70c and L1*L2 = 99c - you have a 1% chance of winning $70 and a 99% chance of losing $1.  In a lottery scenario the prizes will never exceed the take so the expected gain would not exceed the expected loss such that you wouldn't get a "Yes lets go" decision from this model in that scenario.

What you've attempted here is a mix of financial models.  Ordinarily an expected gain is calculated using Expected_Outcome = Exp_Gain - Exp_Loss which you have covered.  But you have introduced other conditions.  Provided the bases are consistent I wouldn't be concerned about $ or %'s.  The point Oaktree touches on is the ROI philosophy which is also important - if the timeframes are long enough should discounted cash flows be taken into account?

Can I ask the context for this question?  It appears to be an investment decision model (I could be wrong) - depending on the type of investment there may be other loss minimisation strategies available.  Also, depending on the context there are a number of investments that could meet your criteria but there maybe other non-financial factors that should be considered.

Just my thoughts.....
Andrew


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## Oorang (Jan 10, 2007)

Context... Well... Sure  But I warn you it's dumb.

Believe it or not all this started over a conversation about which store to go to. We needed a special screw for a door handle. We knew for fact the hardware store would have it, but it was 20 minutes away. We THOUGHT the deparment store 5 minutes away might have it. So the question became. But if the close store did not have it, it would tack on the extra drive time to other store (because our house, and the two store form a triangle) PLUS the wasted time looking for the item in the first store. So there were three possibilities. The far store was only a medium travel time, but a sure bet. The second store could pay off by being faster or not. (We went to the close one and it had it.)

And that just got me interested in that TYPE of problem. I was digging around and sumbled across some interesting game theory articles and decided just for fun to formulize the problem. I determined that we had risked 5 minutes for a potential gain of about 25 minutes. And it had paid off. THEN it occured to me that this had much broader application so I started reworking my travel time formula to what you see here. 

I told you it was stupid


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## erik.van.geit (Jan 10, 2007)

took the time to read all this
so taking the time to reply, although the best place to be for me at this hour is my bed
the contrast in this topic is wonderful
in other words
the (anti)climax is fantastic


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## Bartek (Jan 11, 2007)

> I would have through a lottery situation would never pass the (G_1*G_2)>(L_1*L_2) test given not all of the take is returned as prizes.



By "lottery" I mean any prospect with high skewness, i.e., small probability of large gain and large probability of a small loss, not necessary real "state lotteries". In fact, sometimes even "real world" lotteries may feature tickets with positive expected value - in case of multiple rollovers or due to heavy bias (not uniform distribution) in numbers selected (classic 6/49 lottery is a form of parimutuel bet, you are playing against other players, not the lotto company).

The problem with decision models that rely on criteria other than expected values is that they are sometimes very inconsistent. For example, it was proven axiomatically, that if a person rejects the following bet: 50% probability to win $105 and 50% probability to lose $100, such a person should also reject (on the standard principle of the convexity of utility function) a 50-50 bet of losing $4,000 and winning $400,000


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## Oorang (Jan 11, 2007)

> For example, it was proven axiomatically, that if a person rejects the following bet: 50% probability to win $105 and 50% probability to lose $100, such a person should also reject (on the standard principle of the convexity of utility function) a 50-50 bet of losing $4,000 and winning $400,000


 Do you mean that they _will_ or they _should_?


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## just_jon (Jan 11, 2007)

Kinka surprised Nate, and maybe Tushar, haven't joined in -- financial risk/reward == Nates ballpark, TM's a whiz at probability theory as I recall ...


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## Bartek (Jan 11, 2007)

> > For example, it was proven axiomatically, that if a person rejects the following bet: 50% probability to win $105 and 50% probability to lose $100, such a person should also reject (on the standard principle of the convexity of utility function) a 50-50 bet of losing $4,000 and winning $400,000
> 
> 
> Do you mean that they _will_ or they _should_?




They should if they make consistent choices on the basis of standard principles of utility theory. In practice, they won't, of course


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