Assumptions for Multiple linear regression

1. Relationship between dependent variable and independent variables is linear.
2. There is no linear relationship between independent variables and they are also not random. If there is linear relationship between independent variables, it is called Multicollinearity leading to high R^2 and significant F Stat. This results in inflated Std Err and low T Stat ( opposite of heteroskedasticity effect).
3. Expected value of Error term is 0 and Error term is normally distributed.
4. Variance of Error term is the same for all observations. If this assumption is not true, it is called Heteroskedasticity.This can be tested by Breuch Pagan test. If there is Heteroskedasticity . , then Fstat is unreliable and SError is understated and T stat is overstated.
5. Error term is uncorrelated across observations. If it is correlated, then it is called Serial Correlation. This is tested using Durban Watson (DW) test. Here F stat and T stat is too high. DW = 2(1-r)

Correlation

How does the nature of the dependent variable vary based on the independent variable ? – This is explained by taking a sample of the population and computing Covariance.

This just shows if the two variables are positively related (or) negatively related (or) not related at all.

Assuming x is independent and y as dependent, have a number of observations and plot scatter diagrams for visual view.

Covariance = Sum of (( x – x bar) ( y – y bar)) / (n-1)

For Covariance to be applicable cov(x,y) = cov(y,x) and Cov(x,x) = variance (x).

The sample correlation coefficient is derived from sample Covariance so it can be used as a unitless measure to compare apples to apples.

Correlation Coefficient = Cov(x,y) / std x . std y

std x = sqrt(sum(x – x bar)/ n-1 )

LIFO Reserve Basics

A good video that explains LIFO Reserve Basics

Points to Note

LIFO Inv + LIFO Reserve = FIFO Inv

For the next year

LIFO Reserve = Prev year’s LIFO Reserve + ( LIFO Cogs – FIFO Cogs)

To make it easy to digest, we can rearrange the above and state as

LIFO Cost of good sold = FIFO Cost of goods sold + ( Change in LIFO reserves)

Eg

Year 1 — LIFO Inv = 200, LIFO Res = 100, then FIFO Inv = 300

Year 2 – If LIFO Cogs = 400 and FIFO Cogs = 50, then this difference is 350. This is to be added to the opening balance of LIFO Reserve which is 100 resulting in the new LIFO Reserve for year 2 as 100 + 350 = 450.

When LIFO method is used in US GAAP, the LIFO Reserve needs to be reported as well to signify the reserve or additional inventory had the FIFO method was followed ( in an environment of increasing inventory cost).

When LIFO liquidation happens, LIFO is selling more goods that was bought at lower cost , thereby increasing gross profit. Gross profit due to LIFO liquidation =( # of units liquidated) * (Replacement cost of the units liquidated – historical purchase cost of those units).

Good reference link for Inventory related topic.

Understanding of Spot Rate, Forward Rate and Forward Price Calculation

This is a good video that explains in simple terms the Spot Rate, Forward rate and forward price from CFA Level 2 perspective.

Eg: yr1 spot rate = 3%, yr2 = 4% yr3 = 6%

Assuming FV = \$1000 and a cash flow is \$50 per year, use scientific calculator to compute PV of these cash flows.

Using the PV, the YTM can be obtained.

To obtain forward rates using these spot rates, eg. 1 year forward rate 1 year from now, we can use yr2 spot rate and yr1 spot rate to calculate the result. In other words, if I need to earn 4% overall in 2 years and I am investing at 3% for first year, then what should be my rate 1 year from now for the next 1 year, so I can take the money from year 1 investment and reinvest it at this new rate. Based on no arbitrate theory (1+ yr1 spotrate) * (1+ yr 1 forward rate for 1 yr) = (1 + yr2 spot rate)^2

Trying one or more examples will make this really simple and intuitive.

Put Call Parity

Formula 15.11
c + PV(x) = p + s

Where:
c = the current price or market value of the European call
x = option strike price
PV(x) = the present value of the strike price ‘xeuropean’ discounted from the expiration date at a suitable risk-free rate
p = the current price or market value of the European put
s = the current market value of the underlying stock.

The put-call parity formula shows the relationship between the price of a put and the price of a call on the same underlying security with the same expiration date, which prevents arbitrage opportunities. A protective put (holding the stock and buying a put) will deliver the exact payoff as a fiduciary call (buying one call and investing the present value (PV) of the exercise price).

For the exam, you should know that a protective put = fiduciary call (asset + put = call + Bond)

Source : Investopedia.

Eg: Rearraging the above formula, if I buy a protective put and also sell call option, that results in equation

x = asset + put  – call. where x can be strike price of bond or cash, which will be a constant, thereby proving the put call parity.