Friday, July 07, 2006

Investment Strategies


Safe and Stable Investments- Buy Treasury Bond/Notes

Personal Perspective:

The long term Bond interest rate is standing at 5.12%, which I feel has reached its peak. With economy showing the sign of slowdown and unencouraging job reports I feel that Fed has reached the limit for its rate increase. The maximum upward moment on short term interest rate is 25 basis points, if at all there is any upward moment. However, history has shown us that this rosed interest rates cannot sustain for long time. In my analysis I think that Fed would start decreasing interest rate in a year from now.

Correlation between short term and long term

The short term and the long term interest rates are highly correlated. The long term interest rate has drift and diffussion (volatility) component to it but it is still very correlated to the short term interest rate.

Saturday, June 24, 2006

Finance 101: CAPM, Active v/s Passive Fund Management

During my Introduction to Corporate Finance course, I got interested in CAPM dervied by Dr. William Sharpe. I wanted to know the crux of it in detail and I found an excellent article mentioned below. This article describes the fundamental of CAPM...

Capital Asset Pricing Model

Active Fund Management v/s Passive Fund Management
During my course work @ Haas I was explained by my professor that in "long term an actively managed fund cannot beat a passively managed indexed fund". He explained me the rational behind it in details and I kind a nod my head stating that I understood it very well. However, I was puzzled by this statement and wanted to know the arithmetic behind it. Here again Dr. William Sharpe came to my rescue. I found a nice paper by Dr. Sharpe that gives mathematical rational behind those statments utterred by my professor.

The article can be downloaded by clicking the following link
The Arithmetic of Active Management

Finance 101: Modern Portfolio Theory

For details and excellent overview of Mordern portfolio theory about with the CAPM please refer to the excellent article by clicking the link below:

Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolio, and how an asset should be priced given its risk relative to the market as a whole.

The basic concepts of the theory are Markowitz diversification, the efficient frontier, Capital Asset Pricing Model (CAPM) and Beta cofficient, the Capital Market Line and the Securities Market Line.

Finance 101: Present Value of Prepetuities, Annuities

Once we know the cash flow pattern we simply discount each payment by its appropriate discount factor

Consider an investment that pays a cash flow of CF in perpetuity. Then the present value of the cash flow is given as
PV = CF/r
r is the interest rate (also know as opportunity cost of capital)

Growth: Suppose the constant perpetuity payment grew at a per-period rate of g….
Cash flow at the end of 1 period = CF, CF2 = CF*(1+g), CF3 = CF*(1+g)*(1+g) and so on....
In this case the Present Value of Cash Flow is

PV = CF/(r-g)

Annuity is a payment or cash flows that are made for a particular period in future. For instance the 30 year mortage payment is a type of annuity for 30 years.
For instance
Consider a $4 annuity due in 4 periods with the interest rate of r per period. The present value in this case is given as

PV = $4/(1+r) + $4/(1+r)^2 + $4/(1+r)^3 + $4/(1+r)^4

In order to derive an equation for perpetuity we could consider the scenario where we split the above payments into 2 parts
  1. Case A: Consider a $4 perpetual payment starting 1 year from today. Here the PV = $4/r
  2. Case B: Consider a $4 perpetual payment starting in 5 year from today. Hence if you stand at year 4 it looks like a perpetual cash flow. Thus value of this payments at Year 4 is $4/r. We know that any cash flow in future can be discounted back to present value by using the discount factor for that period. Thus the present value of the perpetual cash flow in year 5 is given by Value of Cash flow at year 4 * Discount Factor for 4 years. PV = $4/r * 1/(1+r)^4

We could replicate our original payments of $4 per period of 4 period by subtracting the payments from Case A with payments from Cash B. In other words, we could obtain the present value of an Annuity by subtracing PV of Case A with PV of Case B.

PV of $4 for 4 period = $4/r * (1-1/(1+r)^4)

In general, PV of annuity with Cash Flow CF till period t is given as

PV = CF/r * (1-1/(1+r)^t)


Suppose the constant annuity payment grew at a per-period rate of g…. Cash flow at the end of 1 period = CF, CF2 = CF*(1+g), CF3 = CF*(1+g)*(1+g) and so on.... In this case the Present Value of Cash Flow is

PV = CF/(r-g) * (1-((1+g)/(1+r))^t)

Finance 101: Net Present Value (NPV)

Present Value: Present value is the $ amount achieved by using the capital markets to transfer cash flow from other dates/events to today (the present).
For instance lets assume if a bank is giving you 10% interest per year, hence in order to receive $1.10 at the end of a year, you need to invest $1.00 today. Thus Present Value of $1.10 one year from now @ 10% interest rate is $1.00

Discount Factor: The factor which discounts the future cash flows to obtain their present value is known as Discount Factor.
For instance,
PV of $1.10 to be received next year = 1.10/1.10 = ‘discount factor’= 1/(1+r).
10% or 0.10 = r is called the 1-year ‘discount rate’ or ‘interest rate.

  1. Now suppose you will receive $1.21 two year from today and interest rate for both year is same (10% per annum). In order to find the discount factor, we need to think about Present Value of $1.21 that is to be received 2 years from now. We can split the 2 years into 2 duration of 1 year and find the value at the begining of each year. Once we have value at the end of Year 1 we can get the Present Value.
  2. Thus value of $1.21 (received at year 2), a year from now, i.e. at end of Year 1 = 1.21/(1+r). But we also know that the Present value of CF a year from now is CF/(1+r) or CF * Discount factor for 1 year.
  3. Present value of the cash flow = Value of CF at year 1 * Discount Factor for 1 year, which is equal to (1.21/(1+r)*1/(1+r) = 1.21/(1+r)2. From this we can compute the discount factor for year 2 as 1/(1+r)2.

General For Cash Flow in period t, PV = CF/(1+r)t. -r is the per period interest rate and t is the number of periods.

  • For Cash Flows in several periods, C1, C2, C3, ....

PV = C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + .........


NPV is the PV of all cash flows including the initial (out) flowof the investment, C0

NPV = Co+ C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + .........

With a capital market all investors can agree on the ranking of projects.

NPV Rule: Invest if NPV > 0

Equivalent rule: Invest if Present Value of future Cash flows > Co (Initial Cash outflow)