Some useful concepts in Actuarial Science

(including some funny expressions!)

- ADITYA MOHAN MATHUR

The list below is based on my understanding of the subject. It is also a reflection of what I sometimes heard from my teachers. I am grateful to all of them!

Mathematics + Common Sense = Statistics

Statistics + Sharper Common Sense = Actuarial Science

 

Financial Mathematics

  • Security/Instrument: device that ties the issuer/ issuing party to a certain set of cash flows
  • Interest for debt is tax-deductible, dividend for equity/preference share is not.
  • Coupon = interest. Its rate is linked to face value
  • Bonds/debentures and equity/preference shares can be listed on an exchange
  • Index linked security: future cash flows linked to inflation index
  • Loan equated installments: any tenure, equal CFs throughout, interest decreases and capital repayment increases with passage of time
  • Accumulation, A(n), is inverse of Present value, V(n)
  • Actuarial risk is risk of not meeting an obligation when it falls due
  • Interest (i) is paid in arrears, discount(d) is collected in advance
  • Best deal is to borrow on simple interest and lend on compound interest ( at a rate not lower than simple interest rate)
  • Nominal interest= convertible interest = = interest payable p times per year
  • Accumulating factor= effective rate = compound rate = /p
  • Force of interest = interest payable continuously = ln (1+i) = instantaneous rate of interest
  • i > > ln(1+i) >  >
  • (1+effective rate) = (1+inflation rate) (1+real rate)
  • Immediate annuity payable in arrears/advance/continuously = sum of CFs discounted in arrears/advance/continuously
  • Classifications of annuities: 1) immediate or deferred 2) level or increasing or decreasing or customized 3) annual/monthly or, in general, pth ly 4) certain or contingent 5) in arrears or in advance or payable continuously
  • 1 year = 365.25 days = 52.18 weeks
  • Interest rates and bond prices are inversely related
  • APR= annual percentage return is slightly less than two times of Flat rate
  • Flat rate of interest: is simple rate of interest charged on the original amount borrowed for the entire repayment period whereas APR: rate of interest charged on reducing principal amount( reduced by the extent of capital repaid)
  • Payback period: length of time required to recover initial investment without considering interest. If interest is considered it is known as Discounted payback period. Both ignore cash flows after PP/DPP is reached.
  • IRR= internal rate of return from project = rate at which NPV of that project = 0. Generally, if IRR > WACC, project is acceptable
  • Cross over point = rate @ which NPV of 2 projects is equal
  • MWRR: yield earned on the fund over the period by taking into account cash flows and their timings
  • TWRR: also takes into account the growth factors of the CFs in addition to the requirements for MWRR, hence a better indicator of fund manager’s performance
  • Running yield = Coupon rate/ Price of Stock
  • If redemption value > cost price, there is Capital Gain. These can be offset against losses in same year
  • Real yield: yield after adjustment for inflation
  • Equity price inclusive of next dividend is cum dividend price and exclusive of dividend just paid/ immediately payable is Ex dividend
  • Arbitrage opportunity: opportunity to make a risk-free profit
  • Hedging: strategy to minimize future loss
  • Spot rate: rate currently prevailing in the market
  • Forward rate: rate expected to prevail at a future date
  • Factors affecting interest rates: demand, supply, base rates, inflation, money supply, tax rates, rates in other countries
  • Longer dated bonds are more sensitive to interest rate movements comparatively
  • Effective duration/volatility and duration/ DMT: measures for interest rate sensitivity, found out by differentiating PV equations w.r.t. discount rate. They provide measure of life of an investment.
  • Convexity: shows spread between times of payments, double derivative
  • Annual growth factors ~ lognormal distribution

We are proud to announce FOUR more Actuaries (qualified in the second half of 2017) from amongst our alumni:

1. Jinal Pandit Sheth, Fellow of Institute of Actuaries of India and Institute and Faculty of Actuaries, UK 

2. Kshitij Shah, Fellow of Institute and Facuty of Actuaries, UK

3. Krithika Verma, Fellow of Institute of Actuaries of India

4. Siddarth Narayan, Fellow Actuary of Institute and Faculty of Actuaries, UK. 

You can read Reviews by our alumni and students at the link:
Read Reviews

Hearty Congratulations to

[1] Kshitij Shah for standing First in CA3 examination held by Institute of Actuaries of India in July, 2017

[2] Albina Chettiar for securing highest marks in the subject of ST2 in the examination of institute of Actuaries of India held in September, 2017.

Congratulations to all our students for putting up an excellent performance at IAI exam. held in September, 2017 and IFoA, UK held in October, 2017
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