Expected Value and Probability Distribution | EV, PD | Sample Exercises

Probability Distribution indicating the sum of possible events in one specific case which affecting the mean of returns. Possible event may occur at least from 2 up and the total always equal 100% or 1. 1 is each case of complete events. Each percentage of possible event (P) will help to define the together possible value from each event (return - R) to calculate Expected Value (or sometimes they call expected returns).

The formula or Probability distribution is: PD = P(1) + P(2) + ... + P(n)

• Where P is percentages (%) each possible event may occur
• And n is number of event may occur
• P(1) + P(2) + .... + P(n) = PD =100% = 1

The formula or Expected Value is : EV =  R(1).P(1)  + R(2).P(2)  + .... + R(n).P(n)

• Where R is return from each possible event, i.e. R(1) is return from event (1) or P(1)
• Ev is currency, R is currency, while P is percentage.

Please try the following sample exercises ! The answer is attached in the videos . 

1. In case of you will receive approximate revenue from your invested with Company A $130,800, with Company B $22,600, with Company C $140,600, and with the Company D $80,000. By assuming that, the probability distribution is 25%, 30%, 30% and 15% respectively. Please calculate Expected Value (Return)?
2. Mr. Bona is earning from Instance payment online system, called “JustBeenPaid.com”. He owns 10 shares on this website. To get paid 100%, he has to click on 10 advertisements (Advs) per day.  If he clicks 6 Advs, he will get paid $ 60.00 per day. If he is so busy, he clicks only 3 Advs, so he will get paid $ 30.00. Otherwise, he is so tired and sleepy, he clicks only 1 Advs, he will get only $ 10.00. 
        a) Please find percentage of clicking 6 Advs-P1, click 3 Advs-P2, and click 1 Advs-P3 ?
        b) Please find Expected value from each share ?
        c) Please find Total Expected value from all his shares ?
3. Somaly is known as top selling Dell Laptop during exhibition 2012 at Sorya super market. Today, she joins the DELL generation at RUPP. She is asked to sell new arrival products. The possible hot sale product is DELL Vostro and Inspiron. We consider if she could sell up to %65, it means she can earn about $4500.00. If she can only achieve medium sale is 22%, she might earn only $2800.00. However, the lowest sale might be at $ 1150.00.
         a) Please find percentage of return from lowest sale (P3) ?
         b)  Please define the expected value (EV) of DELL selling by Somaly ?

The answer is attached in the videos .   

 

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Investing RISK

There are many ways to handle Risk in Investing. The standard risk management are: avoidance, acceptance, transferring, and reducing. Risk is always stick with returns where investors know that "the more return they receive, the higher risk they will face." From the concept of facing with Risk, investors should consider on their investment by:

• Setting up clear goal
• Setting up possible returns
• Understanding Risk in Investment
• Setting up Financial Planning and Reviewing periodically
• Setting up Retirement Plan
• And Risk Policies (team and management).

How much you understanding about Investing Risk ? 
The following video will let you know and capture some knowledge about investing risks with example of International Stocks and graph of Return defining level and possibility of Risk you might face (Risk and Returns):

1. Stock : Large Stock, small stock, preferred stock, common stocks
2. Bond : Government bond, long term, short term, company bond, ... etc.
3. Bills : Treasury bill, commercial papers, ...etc.

How to Handle Risk : Free ways 
The four step of handle risk is easy to understand as the following. We using standard management in avoiding, accepting, transferring, and reducing:

1. Risk Avoidance: avoiding any activities concerning to risk or willing to happen. For example, drunk drive causes traffic accident, then should not drive when drunk.
2. Risk Acceptance: accepting any risk that willing to happen and categorize them into group, types, small plot, and decide how to deal with it.
3. Risk Transferring: investors sometimes can transfer some risks to other agency to handle it (i.e. buying insurance, external auditors, outsourcing teams, ...) or might make the risk to other opportunities. 
4. Risk Reducing: Some risks are bigger and larger affecting investing, so they reduce them into small cap and decide how to fight it with it from a way of accepting, then transferring, avoiding, or dealing by themselves.

For more lessons click here !

Investment:Important?

When talking about Investment, people mostly understand about the concept of "Earning". However, investment means to many things more than earning dollars. The investing can be saving, giving away, improving, increasing, or making better change. The term of investment in types as private and public is clearly begun using financial capital and human capital the same, but different in return. That is why people ask how important of investment. Today, an investment to be described is Private Investment which consist of the follow main concepts to get to know, understand, and keep as knowledge:

1. Capital Market
   
   Any market which most consider on raising fund from financial markets : securities market, stock, bond, and other commercial markets. There are 4 types of capital market:    
   • Primary Market: first issuer is first borrower, selling to investor as first buyer or lender.
   • Secondary Market:
   • Auction Market: market selling products in bidding process: Bid price up from the lowest price to the higher where customers possible to offer. Bid price-down from the set estimated price down to the lowest one where customer possible to offer (normally for public investment, project, etc.)
     
     
                   
     
     
   • Negotiated Market: a market between seller and buyer negotiate the possible price with / without middle man. If with middle man (he or she will receive commission, percentage, or some parts of ownership, i.e. shares).
   • Capital market is important in financial operation, expanding business, business and government raising fund from selling stock and bond, and improving people welfare.
2. Reasonable Expectation
   
   • Investor expect high return, where high risk is coming along.
   • Investors should consider on: setting possible expectation, setting possible goals, study risk policy, financial planning (FP), and set retirement planning.
     
                      
3. Knowledge and Experiences
   • How important of knowledge, experiences, and capital toward investment?
   • Knowledge: skills, set goal, FP, risk and reward, asset allocation, market diversification, ...
   • Experiences: history of work, testing, decision making, and also professions helps
   • Capital: financial and human capital
4. Preference and Risk Tolerance
   • Prefer high return = high tolerance (facing to deal with problem)
   • Prefer low return = low tolerance (earn little by little or sometime drop it)
   • Prefer medium return = be flexible to accept / face risk (deal with it step by step, or if too much drop the return for surviving first).
     
                 
5. Probability Distribution
   
   • Probability distribution allowing to sum up all possible event (P) may occur in one exact case
   • Probability distribution (PD) = P(1) + P(2) + ... + P(n)
   • PD = 100%
   • PD help to define Expected Value (we set possible expected returns from one exact case / period)
   • Expected Value (EV) = R(1).P(1) + R(2).P(2) + ... + R(n).P(n)
   • Detail, PD and EV click here ! with some example exercises.
6. Bond Price and Interest Rate
   • Bond Price has components: yield to maturity (YTM), interest return, number of period investing, Par value
   • There are many components associated with PB such as discount rate, inflation rate, market risk rate, etc.
   • See formula of PB and exercises, click here !
     

Download Full lessons here - Chapter Three (Important Investment Concept) !