{"id":15617,"date":"2025-06-10T08:52:31","date_gmt":"2025-06-10T08:52:31","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=15617"},"modified":"2025-06-10T08:52:32","modified_gmt":"2025-06-10T08:52:32","slug":"the-standard-deviation-of-exxon-bonds-that-pay-12-for-50-percent-of-the-time-and-8-for-the-other-half-of-the-time-would-be-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-standard-deviation-of-exxon-bonds-that-pay-12-for-50-percent-of-the-time-and-8-for-the-other-half-of-the-time-would-be-2\/","title":{"rendered":"The standard deviation of Exxon Bonds that pay 12% for 50 percent of the time and 8% for the other half of the time would be 2"},"content":{"rendered":"\n<p>The standard deviation of Exxon Bonds that pay 12% for 50 percent of the time and 8% for the other half of the time would be 2.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p><strong>Standard Deviation = 2%<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (Approx. 300 Words):<\/h3>\n\n\n\n<p>To compute the <strong>standard deviation<\/strong> of returns, we need to measure how much the returns deviate from the average (mean) return. The standard deviation is a statistical measure of the dispersion or spread of a set of values.<\/p>\n\n\n\n<p>In this case, we are told that the Exxon Bonds yield:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>12% return 50% of the time<\/strong><\/li>\n\n\n\n<li><strong>8% return 50% of the time<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Calculate the <strong>Mean (Expected Return)<\/strong><\/h4>\n\n\n\n<p>The expected return \u03bc\\mu is the weighted average of all possible returns. \u03bc=(0.5\u00d712%)+(0.5\u00d78%)=6%+4%=10%\\mu = (0.5 \\times 12\\%) + (0.5 \\times 8\\%) = 6\\% + 4\\% = 10\\%<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Calculate the <strong>Variance<\/strong><\/h4>\n\n\n\n<p>Variance is the average of the squared differences from the mean: \u03c32=0.5\u00d7(12%\u221210%)2+0.5\u00d7(8%\u221210%)2\\sigma^2 = 0.5 \\times (12\\% &#8211; 10\\%)^2 + 0.5 \\times (8\\% &#8211; 10\\%)^2 \u03c32=0.5\u00d7(2%)2+0.5\u00d7(\u22122%)2=0.5\u00d70.0004+0.5\u00d70.0004=0.0002+0.0002=0.0004\\sigma^2 = 0.5 \\times (2\\%)^2 + 0.5 \\times (-2\\%)^2 = 0.5 \\times 0.0004 + 0.5 \\times 0.0004 = 0.0002 + 0.0002 = 0.0004<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Calculate the <strong>Standard Deviation<\/strong><\/h4>\n\n\n\n<p>\u03c3=0.0004=0.02&nbsp;or&nbsp;2%\\sigma = \\sqrt{0.0004} = 0.02 \\text{ or } 2\\%<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Interpretation:<\/h3>\n\n\n\n<p>The standard deviation of 2% means the returns of Exxon Bonds vary by about 2 percentage points above or below the average return (10%). Since the return alternates between 8% and 12% with equal probability, it creates a symmetrical distribution around the mean. A 2% standard deviation reflects this regular fluctuation and is a relatively low level of risk, indicating the bond&#8217;s returns are predictable within a narrow range.<\/p>\n\n\n\n<p>This simplified calculation assumes only two possible outcomes with equal probability, making the math straightforward and suitable for basic investment risk analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The standard deviation of Exxon Bonds that pay 12% for 50 percent of the time and 8% for the other half of the time would be 2. The correct answer and explanation is: Correct Answer: Standard Deviation = 2% Explanation (Approx. 300 Words): To compute the standard deviation of returns, we need to measure how [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-15617","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=15617"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15617\/revisions"}],"predecessor-version":[{"id":15618,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15617\/revisions\/15618"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=15617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=15617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=15617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}