ACTL1101 Lecture Notes - Lecture 5: Standard Deviation, Gzip

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bluebee342

22 Oct 2018

School

UNSW, UNSW Sydney

Department

Actuarial Studies

Course

ACTL1101

Professor

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Document Summary

# load the package install. packages("moments") library("moments") total1 % summarise(avg = mean(grosslossbuilding), # find the standard deviation skewness = skewness(grosslossbuilding)) # find the skewness claims % group_by(georisk) a % summarise(num_claim=n()) a. # find the claims in group of georisk policies % group_by(georisk) # find the policies in group of georisk total2 % mutate(claim_pppy=num_claim/num_policy/10) # calculate the average claims per policy per year. Content type "application/x-gzip" length 5686536 bytes (5. 4 mb) downloaded 5. 4 mb. The following objects are masked from (cid:528)package:stats(cid:529): filter, lag. The following objects are masked from (cid:528)package:base(cid:529): intersect, setdiff, setequal, union. Content type "application/x-gzip" length 54657 bytes (53 kb) downloaded 53 kb. > # find the claims in group of georisk. > # find the policies in group of georisk. > # calculate the average claims per policy.

Related Questions

Ralph and InventoryManagement

During discussions, Ralph, our hospital stockroom managergestures proudly at the ceiling-high stocked warehouse and statesthat he has never had to turn away any request for any item. Inother words, he is providing his users 100% CSL (cycle servicelevel). We ask him what the average lead times are for the mostused meds and he responds âwithin 3 days for most itemsâ. He thengoes quiet, as the implications of what he has just said sink in âwhy keep so much inventory of everything when replenishments areonly 3 days away? Well, he says defensively, after a pregnantpause, âAs I said, I have never had to turn any user away and youdonât know how wildly variable demand can be in a hospitalâ. Sure,we think, but not so variable as to call for a warehouse full ofmed items! Letâs help Ralph out.

- Pick a few âAâ or vital SKUs from inventory,based on importance in terms of sales, profits, stockoutconsequences to customers, or cost of holding.

We pick a high cost and vital item, heart stents, with uncertaindemand.

- Find out the current formal inventorypolicies, if any, in use for those items (and when these wereset).

Ralph uses a continuous inventory management system forstents:

Order size: 300 units per order

ROP: 200 units (inclusive of safety stock of 50 units), i.e.,order whenever the inventory position falls to 200 units

- Find out whether these policies are beingfollowed.

Ralph confirms that he inherited these policies and followsthem.

- Ascertain current operational inventorymanagement parameters.

Ralph provides the following estimates:

Holding cost H = 25% of item cost

Ordering cost S = $100/order

Current supply lead times LT: 3 days stable

Average daily demand d: 50 units/day

Standard deviation of daily demand Ï_d:3units

Actual customer cycle service level: 100%

Item cost: $1000/unit

Assume 365 working days in a year

1. Develop recommended order size (EOQ) and aROP for the selected SKU using the above current operationalinventory management parameters. Maintain CSL at 100%.

a) Recommended EOQ = ? units

b) Recommended ROP = ? units

EOQ = â (2*D*S)/H; where D = Annualdemand; S = Cost of placing one order; H = Cost of holding 1 unitin inventory for 1 yr

ROP = d * Leadtime + Safety Stock

Safety Stock = z value correspondingto CSL of 100% * Ï_d âLT;

where d is average daily demand,Ï_{d =} standard deviation of demand, LT = leadtime

# of orders/yr= D/EOQ (order qty)

2. Compute and show the differences inrecommended order size, ROP, and total costs for the selected SKUvs. current figures.

Current System

Total cost = TotalHolding Cost + Total Ordering Cost

= Avg Inventory * H + # of Orders/yr *S

= Avg Inventory * H + (D/Order Qty) *S

= ?

Average Inventory = ? units

Recommended System

Total cost = ?

Average Inventory = ? units

Total cost saving with recommendedsystem comparted to current system= $?

Capital investment avoided = ? (fromreducing average inventory @$1000/unit)

3. Can we do even better?

a) If Ralph could reduce the current lead time of 3 days to 2days without significant cost increases:

Revised ROP = ? units

Reduced safety stock = ? units

Reduced average inventory = ?units

b) If Ralph could reduce the cost of placing an order (S) to say$50 instead of the current $100/order by migrating the orderingprocess to a web based system:

Revised EOQ = ? units

Which means that:

Revised average inventory = ?units

and,

Revised total costs = $?

c) Anything else Ralph can do tolower the Total Cost?

PLEASE SHOW EVERY STEP OFTHIS PROBLEM PRECISILY WHEN SOLVED SO I CAN UNDERSTAND THE STEPS. IWOULD REALLY APPRECIATE IF THE SOLUTIONS WOULD BE SHOWN OUT STEP BYSTEP

graysheep764

PLEASE ROUND TO 2 DECIMALS! THANK YOU

1.) A company issues a 10 year bond, $1,000 face value, 4.5% coupon rate. If the bond sold for $1,045, what is the Yield to Maturity?

2.) For the bond of question 1, that is a $1,000 face value, 4.5% coupon rate, 10 year bond whose price is $1,045. What will be the price of the bond at the end of year 5?, assume the YTM does not change.

3.) The question is written here, but in order to be able to give you partial credit, I will ask for sub-sets of the final answer. Question 3 is composed of questions 3, 4, 5, and 6.

A company issues a 7 year bond, 6% coupon rate, $1,000 face value. This bond sold for $970. When the bond was sold the inflation rate was 1.5%, which changes to 2.5% after the end of year 3.

What is the YTM of this bond when it was issued?

4.) What was the real rate when the bond was issued? (Remember, the real rate is the nominal rate minus the inflation rate).

5.) Since the inflation rate is 2.5% after the end of year 3, what is the new nominal rate?

6.) Use the new nominal rate to calculate the price of the bond at the end of year 3.

7.) For questions 7 through 14, use the following averages and covariance matrix.

AVERAGES

	sp500	A	B
Average	-0.0069	0.0018	0.0015

covariance matrix:

	Sp500	A	B
Sp500	0.00336
A	0.00322	0.0041
B	0.0044	0.00514	0.00824

For a portfolio formed by 40% in the SP500 and 60% in A. Calculate the return on the portfolio.

8.) Using the covariance matrix from question 7, calculate the variance of the portfolio formed by 40% in the SP500 and 60% in A.

9.) Using the variance from question 8, calculate the standard deviation of the portfolio formed by 40% in the SP500 and 60% in A.

10.) Using the average and standard deviation from previous questions, calculate the Sharpe ratio for the portfolio formed by 40% in the SP500 and 60% in A.

11.) Using the averages from question 7, calculate the average of a portfolio formed by 30% in A and 70% in B.

12.) Using the covariance matrix from question 7, calculate the variance of a portfolio formed by 30% in A and 70% in B.

13.) Using the variance from question 12, calculate the standard deviation for the portfolio formed by 30% in A and 70% in B.

14.) Using the average and standard deviation from previous questions, calculate the Sharpe ratio for the portfolio formed by 30% in A and 70% in B.

15.) Which of the portfolios offer greater return per unit of risk taken?

	a.	The portfolio formed by 30% in A and 70% in B
	b.	The portfolio formed by 40% in the SP500 and 60% in A
	c.	Both give the same return per unit of risk

taupedonkey505

Please provide all your work on the calculations.

Except where otherwise specified, all interest rates are stated as annual rates.

7a. Obtain weekly prices for a stock of your choice for the 5-year period March 1, 2007 through March 1, 2017. The stock must have traded continuously for the entire 5-year period. (Use the adjusted closing prices from the âhistorical priceâ section for the stock from yahoo finance.) The prices must be submitted as part of the exam answers. Assuming the risk free interest rate is between 0.6875% and 1.3125% (but not 1%).

b. Calculate continuously compounded returns on the stock for each week during the last five years.

c. Determine the average weekly return on the stock.

d. Determine the standard deviation of weekly stock returns.

e. Calculate the average annual return and annual standard deviation for the stock.

f. Using the answers to e and assuming each period during of the year has length .00001 (that is, there are 100,000 sub-periods during the year), find a âuâ and âdâ that can be used in a binary model to estimate the periodic upward and downward movement of the stock price.

g. Select as a strike price an even dollar amount approximately 5% higher than the stockâs current market price and determine how many upward stock price movements must occur in the next 9 months in order for a call option to be in the money.

h. Solve for p and p* for a call option on this stock.

i. Use the general binomial model (without constructing a lattice) to determine the price of a 9-month call option for this stock with the strike price selected in part g.

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ACTL1101 Lecture Notes - Lecture 5: Standard Deviation, Gzip

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