## Quant probability question

aroranidhi2004
Finance Junkie
Posts: 41
Joined: Thu Oct 16, 2014 4:51 pm

### Quant probability question

The number of days a particular stock increases in a given five-day period is uniformly distributed between zero and five inclusive. In a given five-day trading week, what is the probability that the stock will increase exactly three days? A) 0.333. B) 0.167. C) 0.600.

If a stock decreases in one period and then increases by an equal dollar amount in the next period, will the respective arithmetic average of the continuously compounded and holding period rates of return be positive, negative, or zero?

A) Zero; zero.

B) Positive; zero.

C) Zero; positiv.

Pls help with this question

aroranidhi2004
Finance Junkie
Posts: 41
Joined: Thu Oct 16, 2014 4:51 pm

### Quant probability question

Can someone plz help with the qns above?

Regards,
Nidhi

edupristine
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Posts: 704
Joined: Wed Apr 09, 2014 6:28 am
1) Here, please focus on the word “uniformly distributed”. Since all the outcomes are uniformally distributed, there is an equal probability of all outcomes.

Now since the possible set of outcomes is:
X = {0,1,2,3,4,5}

Probability of each outcome: Favourable Outcome/Total no of outcomes = 1/6 =0.167
Hence the answer option is ( B ).

Explanation for second Question is given below:

2) Correct Answer: Option ( C )

The holding period return will have an upward bias that will give a positive average.

For example, if a stock falls from \$100 to \$90, the fall is 10% and the rise from \$90 to \$100 is an increase of 11.1%.

Continuously compounded return
Period 1 = ln(90/100)= -0.1054
Period 2 = ln(100/90)= 0.1054
Hence, the average = 0

The continuously compounded return will have an arithmetic average of zero.
Hence holding period return average will be positive and continuously compounded return average will be zero.

aroranidhi2004
Finance Junkie
Posts: 41
Joined: Thu Oct 16, 2014 4:51 pm
Hi,

Thanks a lot for explanation, i have understood 2nd question, but with regard to the explanation to the 1st one, "In a given five-day trading week, what is the probability that the stock will increase exactly three days?" how we are accounting for the probability of three days i.e the stock price will increase for 3 days.

Regards,
Nidhi

edupristine
Finance Junkie
Posts: 704
Joined: Wed Apr 09, 2014 6:28 am

### Quant probability question

Consider the following explanation:

Let X be the event of increase in the stock price.

P(X=0): This means the probability that the stock will increase for 0 days out of 5 days.
P(X=1): This means the probability that the stock will increase for 1 day out of 5 days.
P(X=2): This means the probability that the stock will increase for 2 days out of 5 days.
P(X=3): This means the probability that the stock will increase for 3 days out of 5 days.
P(X=4): This means the probability that the stock will increase for 4 days out of 5 days.
P(X=5): This means the probability that the stock will increase for 5 days out of 5 days.

Now since the probability that the stock will increase in the given five day period is uniformly distributed (or equally likely),

P(X=0) = P(X=1) = P(X=2) = P(X=3) = P(X=4) = P(X=5) = 1/6 = 0.167

So basically we have to find out P(X=3). And the value for P(X=3) = 0.167 as illustrated above.