Performance of Securities

Lesson #4 – Performance of Securities (9/16)

• Just as a review, basically you need to get familiar with the concepts of

• PV/FV and Annuities/perpetuities
• HPR/APR/EAR

• PV/FV/Annuities/Perpetuities are pretty straightforward – just apply the fucking formula – plug in the numbers and BOOM baby problem solved
• HPR/APR/EAR are a bit more complicated so let me explain in a simple conceptualized manner:

1. Before I begin, let me define the concepts using non-finance-fucked diction

1. HPR – your overall return % over a specified period
2. APR – whatever your return is per day/month, we multiply that shit by a corresponding number to make it annualized
3. EAR – what the interest rate would be if we were smack a yearly interest rate.

1. I know it’s still probably confusing as fuck, so the best way is to demonstrate via an example:

Problem 1: I give you $100 today and you pay me $120 in 18 days. What is the HPR/APR/EAR?

1. Find HPR first – fuck the formula just think conceptually; I receive $100 first, then BOOM you later pay back $120. What’s your return?

1. Well it’s fucking simple – your return is $20 which is just 0.2 or 20%

HPR =   =    =  0.2[pic 1][pic 2]

1. Now you find the APR – just think conceptually; you’re being charged 20% interest for 18 motherfucking days. APR is basically asking well if it was not for 18 days but for a fucking year, what would the interest be?

1. Reworded Fill in the blank: 20% is to 18 days as __% is to 365 days.
2. Well it’s fucking simple – divide by 18 (to get the daily) then multiply by 365

APR = 0.2 *  = 4.0556 or 405.56%     <- you’re just dividing by 18 then multiplying by 365[pic 3]

1. Okay so you know that the fucker is charging 20% interest for 18 days but what would it were to be converted in to a compounded-once-in-a-year format? This is NOT The same as APR – if we were to compound this interest rate ONCE in the year, what would it be?

*I know the diff. between APR and EAR is a bit blurry but stay with me here

1. This time you really have to use the formula but the key is that the APR is equal to the quoted rate when applying the formula
2. The m in this case is the factor you multiplied the interest by to get APR. (365/18)

EAR  =   – 1 =   – 1  = 39.3292 or 3,932.92%[pic 4][pic 5]

• There are two statistics used to indicate whether a portfolio’s probability distribution differs significantly from the normal distribution.

• Kurtosis -  Indicates likelihood of extreme values relative to that of normal distribution

• Positive values = higher frequency of extreme values
• 0 = same as normal distribution
• Negative values = lower frequency of extreme values

• Skew – measures the asymmetry of the distribution

• 0 = symmetric with the normal distribution
• Negative values = extreme negative values are more frequent that extreme positive ones.

• I’m skipping a brief topic on time series of return because I doubt it’ll be on the test

Risk Premiums and Risk Aversion

• Risk-free rate is the rate of return that I can earn with 100% certainty (usually referring to investing money in US Treasury bills, money-market funds, or a bank)
• Risk-Premium is the EXCESS return that you can earn by investing money in stocks as compared to risk-free bonds. (This is the EXCESS, not the TOTAL return)
• The key here is that we know exactly how much we’ll get by investing in risk-free assets in the beginning, whereas for stocks, we don’t know what we’ll get until the end of the holding period.
• Assuming that investors are risk-averse they would only invest in stocks if there is a risk-premium – or else they would just invest in risk-free assets.

Sharpe measure (Reward to Volatility)

• A statistic used to rank portfolios in terms of the risk-return trade-off is the Sharpe Ratio

S   =     =  [pic 6][pic 7]

• A risk-free asset would have a risk premium of 0 and a standard deviation of 0.
• A higher Sharpe ratio indicates a better reward per unit of volatility (hence more efficient)
• Sharpe Ratio is good for ranking portfolios, NOT for individual assets.

5.4 – Inflation and Real Rates of Return