Why Diversification Matters: The Portfolio Effect

Every financial planner, blogger, or consultant will ALWAYS say “you need to diversify your holdings.” But why? Wouldn’t a better plan be to just chuck everything into the asset class that expects to yield the highest possible return? It turns out that an important property about different asset classes ACTUALLY matters: the portfolio effect. By investing in different types of assets, the overall risk of the portfolio falls more than you might naively expect. This post will demystify the magic of the portfolio effect by graphically showing what actually transpires when assets are diversified.

Stocks vs Bonds

Historically, stocks yield higher returns than bonds, but come with the drawback that their returns are materially more volatile. While on average, for example, we might expect stocks to increase by 8% per year, there are frequent episodes such as 2001 and 2009 where huge draw downs occur. By contrast, bonds offer lower expected returns but significantly more certain outcomes. It would truly be unusual for bonds to lose 30% of their value year on year. Graphically, this relationship appears as below. Please see this post on distributions if the meaning of this chart is unclear.

The above data is based on stock and bond returns with the following properties:

  • Stocks: Expected return (annually) 8%. Expected standard deviation of returns of 6%. Thus 95% of stock returns will be between -4% and +20%.
  • Bonds: Expected return (annually) 3%. Expected standard deviation of returns of 1%. Thus 95% of bond returns will be between 1% and 5%.

Our financial goals require a return of 5.5% per year, so we’d like to allocate 50% to stocks and 50% to bonds. This gives us our expected return of 0.5 * 8% + 0.5 * 3% = 5.5%. But what happens to the risk? The answer is: it depends on what happens to bond prices when stocks go up and vice versa.

The Portfolio Effect

We now arrive at what makes the portfolio effect a real thing: correlation. Correlation is a number between -1 and 1 that measures how tightly 2 random variables move together.

  • A correlation of 1 means whenever stocks go up, bonds go up, and vice versa.
  • A correlation of -1 means whenever stocks go up, bonds go DOWN, and vice versa.
  • A correlation of 0 means whenever stocks go up, bonds might go up or down. There is no relationship.

Regarded as the safest investment in the world, US Treasury bonds are typically purchased in times of financial duress when a so-called ‘flight to safety’ is underway. During recessions or bear markets, as stocks fall significantly in value, bonds usually rise in value. Thus, we can assume there is negative correlation between bonds and stocks. Let’s suppose it is -0.4. Through simulation, we can produce 1000 years of hypothetical returns that have the stock/bond return properties assumed above with the negative correlation:

When we allocate 50% bonds and 50% stocks in this portfolio, you might expect that the variance of the returns would be the average of the 2 underlying assets, or 3.5%. In actuality, the risk of our new portfolio is only a modest 2.8%. The reason is the negative correlation between bonds and stocks. Whenever one of our assets falls in value, the other is increasing in value to offset the losses. The result from the portfolio effect is we get a portfolio whose return is the average of the two asset classes but has risk that is less than the average of the two assets. The full returns for 500 scenarios are presented in the table in the conclusion.

The driving force can be seen more clearly when looking at the top 10 and bottom 10 results of the portfolio. When stocks are at their worst (returning -5% on average), bonds are outperforming their expected returns. When stocks are performing their best, bonds are underperforming. The inherent dampening mechanism works to insulate the total portfolio return, resulting in a much more stable profile of lifetime wealth accumulation:

 

The Portfolio Effect: Conclusions

Any time a portfolio adds uncorrelated assets to it, the risk of the portfolio falls due to the portfolio effect. Diversification is not just a hollow word uttered by every financial advisor in the world but an actual, statistical property that lowers risk without sacrificing expected returns. Prudent risk management suggests no one should ever exclude bonds or stocks entirely from their portfolios.

 

Appendix: Results of 500 simulations of stock/bond negative correlation.

SimulationStock ReturnBond ReturnPortfolio Return
1-0.0690.044-0.012
2-0.0550.044-0.006
3-0.0510.027-0.012
4-0.0490.045-0.002
5-0.0490.027-0.011
6-0.0470.034-0.006
7-0.0450.037-0.004
8-0.0450.0480.002
9-0.0450.0470.001
10-0.0440.0530.005
11-0.0400.0440.002
12-0.0380.0430.002
13-0.0370.0410.002
14-0.0350.0390.002
15-0.0340.0520.009
16-0.0330.028-0.003
17-0.0320.0370.002
18-0.0310.0440.007
19-0.0310.0400.005
20-0.0280.016-0.006
21-0.0280.0390.005
22-0.0270.0320.003
23-0.0250.0310.003
24-0.0250.0410.008
25-0.0220.0290.004
26-0.0190.0420.011
27-0.0170.0260.004
28-0.0160.0340.009
29-0.0150.0350.010
30-0.0150.0210.003
31-0.0150.0370.011
32-0.0130.0480.018
33-0.0130.0460.017
34-0.0100.0210.005
35-0.0080.0330.012
36-0.0070.0330.013
37-0.0050.0430.019
38-0.0050.0380.016
39-0.0050.0440.020
40-0.0040.0250.011
41-0.0010.0410.020
42-0.0010.0530.026
430.0000.0320.016
440.0000.0390.019
450.0010.0200.010
460.0010.0410.021
470.001-0.002-0.001
480.0020.0260.014
490.0020.0450.024
500.0020.0510.027
510.0020.0330.018
520.0020.0330.018
530.0040.0320.018
540.0040.0340.019
550.0050.0230.014
560.0050.0420.023
570.0060.0330.020
580.0070.0290.018
590.0070.0340.021
600.0080.0370.022
610.0080.0290.019
620.0090.0370.023
630.0090.0330.021
640.0090.0390.024
650.0090.0300.020
660.0100.0300.020
670.0120.0380.025
680.0130.0280.020
690.0140.0450.029
700.0150.0550.035
710.0160.0490.032
720.0160.0350.025
730.0160.0310.024
740.0160.0390.028
750.0170.0430.030
760.0170.0400.028
770.0170.0260.022
780.0170.0190.018
790.0180.0200.019
800.0190.0370.028
810.0190.0310.025
820.0190.0300.025
830.0200.0410.030
840.0200.0310.025
850.0210.0370.029
860.0210.0250.023
870.0210.0330.027
880.0210.0290.025
890.0230.0120.017
900.0230.0460.035
910.0230.0360.030
920.0240.0400.032
930.0240.0290.027
940.0240.0280.026
950.0240.0270.026
960.0250.0330.029
970.0260.0330.029
980.0260.0330.029
990.0260.0430.034
1000.0270.0250.026
1010.0270.0330.030
1020.0270.0370.032
1030.0280.0310.030
1040.0290.0210.025
1050.0290.0200.024
1060.0300.0460.038
1070.0300.0410.035
1080.0300.0300.030
1090.0310.0430.037
1100.0310.0390.035
1110.0310.0370.034
1120.0310.0380.035
1130.0310.0130.022
1140.0320.0540.043
1150.0320.0310.031
1160.0330.0180.025
1170.0340.0400.037
1180.0340.0310.032
1190.0340.0310.032
1200.0360.0230.030
1210.0360.0380.037
1220.0370.0450.041
1230.0370.0480.043
1240.0370.0310.034
1250.0370.0260.032
1260.0390.0310.035
1270.0400.0320.036
1280.0400.0140.027
1290.0410.0170.029
1300.0410.0330.037
1310.0420.0340.038
1320.0420.0380.040
1330.0430.0200.031
1340.0440.0340.039
1350.0440.0320.038
1360.0440.0360.040
1370.0440.0220.033
1380.0450.0380.042
1390.0450.0330.039
1400.0450.0150.030
1410.0450.0410.043
1420.0450.0380.042
1430.0460.0420.044
1440.0460.0480.047
1450.0460.0260.036
1460.0470.0400.044
1470.0470.0340.040
1480.0470.0210.034
1490.0470.0220.034
1500.0470.0280.038
1510.0470.0420.044
1520.0480.0480.048
1530.0480.0270.037
1540.0480.0360.042
1550.0480.0190.034
1560.0480.0300.039
1570.0490.0330.041
1580.0490.0140.031
1590.0490.0240.036
1600.0490.0420.046
1610.0500.0260.038
1620.0500.0390.045
1630.0510.0380.045
1640.0510.0270.039
1650.0510.0310.041
1660.0520.0360.044
1670.0520.0390.046
1680.0520.0170.035
1690.0530.0150.034
1700.0530.0270.040
1710.0530.0350.044
1720.0540.0350.044
1730.0540.0310.042
1740.0540.0310.042
1750.0540.0230.038
1760.0550.0310.043
1770.0550.0320.043
1780.0550.0120.033
1790.0550.0350.045
1800.0550.0350.045
1810.0560.0370.046
1820.0560.0410.049
1830.0560.0280.042
1840.0560.0380.047
1850.0570.0270.042
1860.0570.0350.046
1870.0570.0370.047
1880.0570.0310.044
1890.0570.0230.040
1900.0580.0170.038
1910.0590.0260.043
1920.0590.0210.040
1930.0610.0460.054
1940.0610.0270.044
1950.0620.0140.038
1960.0620.0280.045
1970.0620.0400.051
1980.0620.0400.051
1990.0630.0370.050
2000.0630.0290.046
2010.0630.0530.058
2020.0640.0470.056
2030.0640.0240.044
2040.0640.0380.051
2050.0640.0350.049
2060.0640.0420.053
2070.0650.0380.051
2080.0650.0360.050
2090.0650.0230.044
2100.0650.0340.049
2110.0650.0280.047
2120.0660.0280.047
2130.0660.0290.048
2140.0670.0340.050
2150.0670.0420.054
2160.0670.0210.044
2170.0670.0280.047
2180.0670.0260.047
2190.0680.0210.044
2200.0690.0400.055
2210.0700.0190.044
2220.0700.0260.048
2230.0710.0270.049
2240.0710.0290.050
2250.0710.0370.054
2260.0720.0490.060
2270.0730.0080.040
2280.0740.0260.050
2290.0740.0330.054
2300.0750.0460.060
2310.0750.0240.050
2320.0750.0320.054
2330.0760.0220.049
2340.0760.0330.054
2350.0760.0390.057
2360.0760.0200.048
2370.0770.0310.054
2380.0770.0330.055
2390.0770.0270.052
2400.0780.0290.054
2410.0780.0260.052
2420.0780.0230.051
2430.0780.0430.061
2440.0780.0220.050
2450.0780.0290.054
2460.0780.0360.057
2470.0790.0510.065
2480.0800.0250.052
2490.0800.0200.050
2500.0800.0280.054
2510.0800.0360.058
2520.0800.0330.056
2530.0810.0290.055
2540.0820.0210.052
2550.0820.0280.055
2560.0820.0180.050
2570.0820.0130.048
2580.0830.0270.055
2590.0830.0210.052
2600.0830.0230.053
2610.0830.0220.053
2620.0840.0290.057
2630.0840.0210.052
2640.0840.0290.057
2650.0850.0260.055
2660.0860.0580.072
2670.0860.0320.059
2680.0860.0340.060
2690.0870.0390.063
2700.0870.0190.053
2710.0870.0340.060
2720.0880.0320.060
2730.0880.0320.060
2740.0890.0390.064
2750.0900.0300.060
2760.0900.0240.057
2770.0910.0570.074
2780.0910.0270.059
2790.0910.0400.065
2800.0920.0340.063
2810.0920.0350.063
2820.0920.0350.063
2830.0920.0460.069
2840.0930.0220.058
2850.0930.0200.057
2860.0930.0310.062
2870.0930.0330.063
2880.0930.0260.060
2890.0940.0330.063
2900.0940.0300.062
2910.0940.0280.061
2920.0940.0230.059
2930.0950.0180.056
2940.0950.0290.062
2950.0950.0010.048
2960.0950.0170.056
2970.0950.0270.061
2980.0950.0420.069
2990.0950.0190.057
3000.0960.0180.057
3010.0960.0380.067
3020.0970.0190.058
3030.0970.0230.060
3040.0970.0390.068
3050.0970.0240.061
3060.0980.0120.055
3070.0980.0350.066
3080.0980.0270.062
3090.0980.0240.061
3100.0980.0130.056
3110.0990.0240.061
3120.0990.0280.063
3130.0990.0310.065
3140.0990.0250.062
3150.0990.0240.062
3160.1000.0320.066
3170.1000.0180.059
3180.1000.0280.064
3190.1010.0340.068
3200.1010.0230.062
3210.1010.0290.065
3220.1020.0280.065
3230.1020.0250.063
3240.1020.0330.068
3250.1020.0340.068
3260.1020.0250.064
3270.1020.0110.057
3280.1030.0290.066
3290.1030.0260.064
3300.1030.0390.071
3310.1030.0240.063
3320.1040.0270.065
3330.1040.0300.067
3340.1040.0390.071
3350.1050.0260.065
3360.1050.0340.069
3370.1050.0420.074
3380.1070.0440.075
3390.1070.0340.071
3400.1070.0260.066
3410.1080.0340.071
3420.1080.0290.069
3430.1080.0480.078
3440.1090.0380.073
3450.1090.0290.069
3460.1110.0290.070
3470.1120.0370.074
3480.1130.0150.064
3490.1130.0340.073
3500.1130.0410.077
3510.1130.0280.070
3520.1130.0250.069
3530.1140.0360.075
3540.1140.0270.071
3550.1140.0210.068
3560.1150.0250.070
3570.1160.0230.069
3580.1170.0190.068
3590.1180.0340.076
3600.1180.0320.075
3610.1180.0400.079
3620.1180.0230.070
3630.1190.0420.081
3640.1190.0180.069
3650.1190.0400.080
3660.1200.0280.074
3670.1200.0400.080
3680.1200.0320.076
3690.1200.0160.068
3700.1200.0190.070
3710.1200.0250.073
3720.1200.0290.075
3730.1200.0380.079
3740.1210.0450.083
3750.1210.0370.079
3760.1210.0240.072
3770.1210.0210.071
3780.1210.0210.071
3790.1210.0350.078
3800.1210.0160.069
3810.1220.0330.077
3820.1220.0360.079
3830.1220.0060.064
3840.1230.0420.082
3850.1230.0290.076
3860.1230.0330.078
3870.1230.0260.075
3880.1230.0450.084
3890.1230.0310.077
3900.1240.0370.080
3910.1250.0130.069
3920.1250.0220.073
3930.1250.0180.071
3940.1260.0140.070
3950.1260.0210.074
3960.1270.0290.078
3970.1280.0250.076
3980.1280.0370.083
3990.1280.0270.078
4000.1290.0160.072
4010.1290.0190.074
4020.1290.0540.091
4030.1290.0090.069
4040.1300.0360.083
4050.1300.0270.078
4060.1300.0250.077
4070.1300.0330.082
4080.1320.0230.078
4090.1320.0260.079
4100.1340.0210.078
4110.1340.0240.079
4120.1350.0380.087
4130.1360.0310.083
4140.1360.0340.085
4150.1370.0310.084
4160.1380.0140.076
4170.1380.0280.083
4180.1380.0310.085
4190.1390.0320.086
4200.1400.0310.086
4210.1410.0370.089
4220.1410.0170.079
4230.1410.0180.079
4240.1420.0310.086
4250.1420.0180.080
4260.1440.0270.085
4270.1440.0440.094
4280.1460.0140.080
4290.1470.0610.104
4300.1480.0400.094
4310.1490.0340.092
4320.1500.0160.083
4330.1500.0170.083
4340.1500.0130.082
4350.1520.0320.092
4360.1530.0170.085
4370.1530.0300.092
4380.1530.0240.088
4390.1530.0230.088
4400.1540.0220.088
4410.1540.0210.087
4420.1540.0190.086
4430.1550.0310.093
4440.1560.0310.093
4450.1560.0030.079
4460.1570.0300.094
4470.1570.0230.090
4480.1580.0250.091
4490.1600.0280.094
4500.1610.0400.101
4510.1610.0080.085
4520.1620.0270.095
4530.1630.0280.095
4540.1630.0260.094
4550.1630.0380.101
4560.1640.0220.093
4570.1640.0350.100
4580.1660.0270.096
4590.1660.0330.100
4600.1680.0130.091
4610.1680.0250.097
4620.1690.0290.099
4630.1700.0320.101
4640.1710.0110.091
4650.1710.0180.095
4660.1730.0140.093
4670.1730.0450.109
4680.1740.0200.097
4690.1750.0200.098
4700.1750.0250.100
4710.1760.0350.105
4720.1770.0470.112
4730.1800.0300.105
4740.1820.0130.097
4750.1860.0050.095
4760.1860.0360.111
4770.1890.0210.105
4780.1890.0290.109
4790.1900.0110.100
4800.1910.0090.100
4810.1920.0110.102
4820.1920.0400.116
4830.1940.0260.110
4840.1940.0230.109
4850.1990.0160.107
4860.2020.0250.114
4870.2040.0220.113
4880.2040.0220.113
4890.2040.0140.109
4900.2060.0020.104
4910.2080.0240.116
4920.2150.0050.110
4930.2150.0100.113
4940.2230.0340.128
4950.2370.0210.129
4960.2390.0270.133
4970.2460.0170.132
4980.2520.0030.128
4990.2550.0350.145
5000.2560.0310.144

1 Response

  1. October 11, 2018

    […] As discussed (again in gory bloody detail) here, diversification works best when assets move in opposite directions to each other. Unfortunately, Joe Average has done the following: […]