TASAS DE INTERÉS 7 (INTEREST RATES): TASA AL CONTADO (SPOT RATE), TASA INSTANTÁNEA (SHORT RATE), TASA A FUTURO (FORWARD RATE), SWAP RATE

Warning: spot rates are calculated by employing Central Bank Treasuries only. So therefore, the first spot rate is the Internal Rate Of Return of such a theoretical zero coupon treasury, the following spot rates -on the yield curve- undergo a bootstrapping process.  Precaución: las tasas de interés al contado se calculan empleando títulos del Banco Central únicamente.  Entonces y por lo tanto, la primera tasa al contado es la Tasa Interna De Retorno de un teórico título sin cupones, las tasas al contado siguiente -sobre la curva de rendimientos- se someten un proceso de iteración/recálculo.


La siguiente es la información después de un día de operaciones en el mercado de renta fija en términos anuales.  The following information is given by the fixed rent market after an annualized trading day (Oct. 11, 2012):

Fecha de vencimiento/                  Spot Rate/Tasa al contado (annual effective):
Maturity Date:

          Feb. 15, 2013                                                        0.1250782%

          Aug. 15, 2013                                                       0.3967851%

         Feb. 15, 2014                                                        0.4751252%

         Aug. 15, 2014                                                       0.5253753%

         Feb. 15, 2015                                                        0.5163284%

         Aug. 15, 2015                                                       0.4922074%

         Feb. 15, 2016                                                        0.3917654%

         Aug. 15, 2016                                                       0.537439%

         Feb. 15, 2017                                                        0.8889277%

Para títulos emitidos por el BANCO CENTRAL.  For "treasuries" issued by the Central Bank.

Cuál es la curva de Tasas Instantáneas?  What is the Short Rate curve ?

Time to maturity in years/Plazo al vencimiento en años: 0.3479452, 0.8438356, 1.3479452, 1.8438356, 2.3479452, 2.8438356, 3.3479452, 3.8465753, 4.3506849 

Habrá que reescribir las tasas de descuento en semestre efectivo y no año efectivo/ You will have to rewrite the rates in effective semesters and not years

La primera tasa instantánea es igual a la primera tasa al contado/The first short rate is equal to the first spot rate:  0.0625195% per semester or 0.0435026% until maturity.  r(0,1)

r(1,2) =  (1.001981961^2 / 1.000625195)-1  =   0.334057%  per semester or 0.2910886% per time fraction

r(2,3) = 0.305232% per time fraction or 0.315497% per semester 

r(3,4) = 0.3277799% per time fraction or 0.337568% per semester

r(4,5) = 0.2433175% per time fraction or 0.239787% per semester

r(5,6) = 0.1873067% per time fraction or 0.185672% per semester

r(6,7) = -0.087239% per time fraction or -0.104445% per semester

r(7,8) = 0.7555578% per time fraction or 0.7785148% per semester

r(8,9) =  1.804683% per time fraction or 1.855504% per semester
The short rate curve tells us the market expectation and the expected value for the 3 month rate in 3, 6, 9, 12 months from now and so on OR the annual effective rate in 1, 2, 3, 4 years and so on...../La curva para tasas instantáneas nos dice la expectativa del mercado de un periodo a otro y el valor de la tasa a 3 meses en 3, 6, 9, 12 meses desde ahora y en adelante O la tasa efectiva anual en 1, 2, 3, 4 años y en adelante ... Ahora la curva de tasas a futuro.  Now the forward rate curve.

f(1,2) = 0.3340567% semester ;  f(1,3) = 0.324776% semester ; f(1,4) = 0.329040% semester

f(1,5) = 0.306719% semester ;  f(1,6) = 0.282498% semester ;  f(1,7) = 0.217904% semester

f(1,8) = 0.2978% semester ;  f(1,9) = 0.491202% semester

f(1,9) = (1.004434805^9/1.000625195)^(1/8)  -1

These are the expected spot rates in 0.6958904 semesters, there is no forward rate for nine semesters.  Estas son las tasas al contado esperadas en 0.6958904 semestres, no hay tasa futura para nueve semestres.

Swap rates or spreads. Tasa swap o márgenes diferenciales:

Given an 8 semester forward rate and an 8 semester spot rate.  (0.491201 - 0.2683594)*100  =  22.28416 bps.  Dada una tasa a futuro para 8 semestres y una tasa al contado para 8 semestres....


Sources/Fuentes:  www.oup.com/us/ppt/derivatives/DMCH13.ppt (David Dubofsky & Thomas Miller)
-Finance By Kay Giesecke from Stanford University
-Financial Engineering & Risk Management By Martin Haugh & Garud Iyengar from Columbia University

BUDGETS & OTHER FORECASTS: DCF ANALYSIS TO APPRAISE DIFFERENT PROJECTS (BANG FOR THE BUCK)

Net Present Value is widely deployed to perform contrast and comparison among projects, proven the discount rate, the life expectancy and the initial investment value are all the same.

Could I use discount cash flow (DCF) analysis to appraise projects with different discount rates, amounts and life expectancies??? YES! But with a twist....

Remember? COST-->BENEFIT or the old fashioned ratio: BENEFIT/COST??

Read the following projects:

year/project	A	B	C	D	E	F	G	H
0	-2000000	-10000000	-10000000	-10000	-110000	-17200	-1000000	-350000
1	1000000	4000000	0	300	25000	10000	200000	35000
2	1200000	4000000	0	500	25000	10000	206000	35000
3	1400000	5000000	14000000	1200	25000	10000	212180	35000
4				2000	25000	10000	218545,4	42000
5				2000	25000	10000	225101,76	42000
6					25000	10000	231854,81	42000
7					25000	10000	238810,46	42000
8					25000	10000	245974,77	42000
9					25000	10000	253354,02	42000
10					25000	10000	260954,64	42000
11						10000	268783,28	42000
12						10000	276846,77	42000
13						10000	285152,18	42000
14						10000	293706,74	42000
15						10000	302517,94	42000
16						10000	311593,48	42000
17						10000	320941,29	42000
18						10000	330569,53	42000
19						10000	340486,61	42000
20						10000	350701,21	42000
21								42000
22								42000
23								42000
24								42000
25								42000

These are the free cash flows for every venture. Each of them has a unique market discount rate above the Cost of Capital related to our Investment Bank.....What is/was the best project overall??

"The Bang For The Buck" is the answer.....The discount rates are as follow (%): 4, 4.1, 4.2, 4.5, 5, 10, 8, 10

We know the present value for CapEx, Costs and Investment. Now we need the present value for the net cash income.....They must be read as :

A= 3315600.82 , B= 11965766.65, C= 12374420.65, D= 14061.80, E= 193043.37 , F= 85135.64 , G= 2450008.29     H= 2144175.17 and now: the ratios of efficiency:

A= 1.65780041, B= 1.196576665, C= 1.237442065, D= 1.40618, E= 1.7549397273, F= 4.949746349, G= 2.450008290, H= 6.126214771 Why investment F has the same discount rate than investment H? Although, F life is shorter than H, F is a high tech venture while H is a monopolic public transport service
**************************************************************************************************************************************

NOW, HOW TO DRAW A BUDGET: In most countries, forecasting the last financial statements by using Customer's Price Index rate of change is bylaw.....There is a major flaw: this rate is an average of the economy as a whole, so it might no mirror the change rates of your business....The alternative: Ground Zero Budget

The author's favorite method:

1. You should calculate the historical geometric average for the change rate of your incomes (both operational and non operational)

2.Apply down analysis to calculate the share for costs, expenses, profit/loss

....Now you can forecast these variables and to draw an income statement with an expected profit/loss

3. The expected profit/loss goes to the EQUITY section on the Balance sheet and again ....based on historical calculations you must apply down analysis to draw the pending values for the accounts on the equity section and the accounts on the LIABILITIES SECTION....The share for each account and subaccount are defined by the arithmetical average of previous years

For example: total income for your company last fiscal year was $150 million.....The historical geometric average for the change is 15% a year

Total operational costs, CapEx and non operational Expenditure. Down Analysis tells us that the historical average weight of them is 80%

150*1.15 = 172 .5 expected total income for next year and 172.5 * 0.8 = 138 the total expected costs, CapEx and non operational expenditure (taxes have been discounted, already)

expected net profit = 34.5 Down analysis tells us that the historical average weight for profits is 50% of the equity

expected equity = $69 millions down analysis tells us that the historical average weight of equity on the financial structure for this company is 70%

liabilites are 30% = expected $29.57 millions

total asset : $98.57 millions

See you around!

Sources: Kay Giesecke, Dmitry Smelov, David Luenberger, Jorge E. Burbano, Alberto Ortiz & Stanford U.

A MULTIPLE CORRELATION INDEX: CORRUPTION AND EXTENSION OF THE ORIGINAL PEARSON PRODUCT (PART 2)

As a follow-up. Here we have got 3 time series featuring 3 different kind of shares. The first share belongs to a fabric corporation, the second share belongs to a petroleum corporation and the third share belongs to a grocery corporation. The skewed Pearson Correlation indexes for each couple are: 0.6651, 0.6727 and 0.6427. Now the raw average price for each trading day:

FABRICS	OIL & GAS	GROCERIES
65,10	3.869,42	24.077,00
68,27	3.860,90	23.843,18
71,08	3.791,27	23.674,54
70,86	3.746,08	23.665,48
69,61	3.698,01	23.084,56
70,91	3.617,88	22.495,30
71,63	3.579,54	22.094,81
71,07	3.621,66	21.910,14
68,17	3.595,94	21.711,46
68,35	3.575,26	21.307,96
69,02	3.597,24	21.226,38
70,87	3.690,66	21.880,14
72,31	3.706,20	22.729,31
71,49	3.699,86	22.932,26
70,44	3.790,14	22.910,22
71,32	3.743,88	23.499,11
72,44	3.740,50	23.422,12
73,95	3.749,48	23.600,99
73,46	3.742,19	23.406,75
73,37	3.738,92	23.806,03
71,75	3.733,71	24.173,57
71,22	3.710,75	24.086,27
70,72	3.694,24	23.794,90
70,97	3.654,79	23.952,48
68,35	3.600,30	23.804,88
71,02	3.643,38	23.920,07
69,56	3.669,10	23.981,40
71,69	3.678,68	24.109,30
73,16	3.702,06	23.275,96
75,38	3.706,62	23.455,27
75,64	3.706,42	23.844,62
72,86	3610,87	23581,93
73,59	3605,19	23347,24
73,2	3623,37	23691,06
74,9	3651,15	23945,73
74,81	3660,14	24018,57
74,02	3619,38	23866,32
74,42	3641,45	23687,05
75,26	3759,57	24152,72
73,89	3856,61	24147,52
74,06	3870,49	22968,05
72,59	3892,56	23028,89
71,37	3873,3	23080,17
71,43	3803,2	22524,51
71,86	3834,58	23072,63
72,88	3884,78	23563,11
74,02	3867,9	23573,5
72,97	3842,18	23059,16
72,42	3818,36	23000,79
73,41	3866,75	22993,5
73,6	3894,27	22867,91
73,41	3976	23010,92
73,82	4069,19	23521,07
72,9	4090,19	23850,26
73,26	4144,15	24071,89
72,75	4081,99	23994,51
71,69	3878,94	23556,18
73,28	3848,36	23504,43
73,27	3836,8	23132,36
74,45	3919,65	23013,05
73,42	3888,22	23005,2
72,2	3926,04	22917,16
71,37	3887,87	22790,82
71,64	3834,56	22889,26
71,49	3774,58	22940,21
71,79	3927,68	22868,54
73,05	3930	22894,61
73,47	3902,05	23020,61
73,45	3915,34	23126,91
72,46	3901,71	23002,63
71,94	3911,94	23014,98
71,91	3900,49	22954,69
70,88	3942,77	22907,7
70,06	3932,33	22786
70,34	3947,59	22737,64
69,22	3951,29	22939,9
71,04	3994,35	23320,87
71,25	4014,27	24242,4
70,51	4027,99	24132,24
71,06	3999,16	23899,82
71,5	4060,33	23954,47
70,97	4044,01	23729,92
70,43	4016,05	23837,89
70,31	3974,01	23793,8
70,09	4010,84	23962,9
71,16	4037,01	24234,67
72,13	4023,77	24221,85
72,95	4066,31	24413
72,3	4046,55	24169,03
72,61	4021,81	24219,63
73,88	4024,89	24229,18
75,24	4012,94	24247,06
75,29	4004,14	24537,92
76,19	3986,96	24893,58
75,41	3981,21	24682,99
74,02	3932,97	24455,89
74,56	3934,09	24438,97
74,22	3874,82	23722,63
74,85	3862,77	23756,54
74,53	3893,18	23765,09
75,59	3994,93	23944,58
76,67	4039,33	23810,71
77,06	4080,31	23797,53
77,48	4110,17	23891,81
77,62	4171,82	24361,05
78,58	4184,78	24687,21
78,94	4103,64	24094,74
79,11	4123,51	24384,35
79,41	4154,09	24422,02
78,26	4142,23	24427,63
79,06	4177,08	24639,66
78,55	4125,09	24376,14
79,34	4144,72	24284,61
80,05	4152,71	24275,73
80,93	4160,73	24352,85
82,21	4190,32	24447,54
82,99	4237,14	24788,28
83,92	4285,22	25196,38
84,17	4286,16	25833,83
83,5	4224,51	25615,49
82,94	4255,18	25325,63
83,34	4280,31	25497,93
83,75	4249,61	25478,48

 

As we explained previously, Both covariance and correlation are measures of SECOND DEGREE. Every isolated line with a product MUST BE turned into its SECOND DEGREE twin. How? Read the following example:

If we know the averages of each set we have to proceed to calculate the differentials as seen on the regular covariance formula. The first line of our "threesome" turns out to be: -8.6254, -34.3924, 409.5620

In order to apply a transformation/conversion we need to use the absolute values. The product of our "threesome" is equal to 121496.645. This is a third-degree value and we need a second-degree one.

121496.645^(2/3) = -2453.0676 Why the negative condition if 2 of the arguments are negative?

RULE OF THUMB: The algebraic law of products is not respected here. We have to apply Boolean Logics. If all of the differentials display the same symbol, the final value is positive. If at least one of the differentials displays a symbol not equal to the remaining arguments, so therefore, the final value is negative.

The skewed covariance is: 3630.2961

The standard deviations of each series are: 3.7080, 185.9578 and 814.4545

Again, the product after the 3 standard deviations has to be rewritten in second-degree

The skewed and consolidated correlation is:

0,5333257994

Why the final value is lesser than the regular coupled-pearson index? We have enhanced the probability space and the number of coincidences are fewer than those watched while our sets are studied as couples.

Sources: RiskCenter, Investopedia, Wikipedia, EdX.org, Coursera.org