))/((( …and other Excel fun.

Of course there’s an Excel formula for mortgage payments…  

It is =PMT(r/12,n*12,PV)

Where:
r = the annual interest rate expressed as a percentage,
n = the number of years of repayment, typically 15 or 30,
PV = the initial amount lent, or present value at t0.

I can’t believe I’ve been using =((r/12)*(1+(r/12))^(n*12))/(((1+(r/12))^(n*12)-1))*PV for a straight year.

Note to self: if a formula seems useful enough that I might want to plug it into Excel, chances are there is dedicated Excel function.

))/((( makes me squint.

Portfolio Theory - Risk Aversion

What is the optimal way to allocate your capital between a risky asset and a risk-free asset?

One way to answer this question is to consider your own risk-aversion; a purely theoretical concept. Risk-aversion has been analyzed in finance, economics and psychology. It tries to quantify your aversion to taking risk, when confronted to uncertainty. And it is noted A.

This is the Utility function: U = E(rp) - 1/2 Aσp2

Where:
U is the utility of your investment,
E(rp) is the expected return of your portfolio,
A is your coefficient of adversity, 
σp is the volatility of your portfolio.

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A Student Loan Repayment Strategy

Student loans can be tricky to repay, especially if you know little about finance, but there are some golden rules that are fairly easy to follow and will save you a lot of time, and money. 

Let’s say for instance that you have 2 loans:
Loan A - $2,000 has an interest rate of 8% per year, or 0.67% per month.
Loan B - $8,500 has an interest rate of 5.5% per year, that is 0.46% per month.

On the very first month of your repayment, the interest for Loan A will be $13.33 while the interest for Loan B will be $38.96. You might be tempted to repay Loan B faster, since it seems to cost you more each month. But it’s not the way loans work; think long term.

Let’s consider that you only repay the minimum payment for loans A & B, over a period of 10 months:

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